Your calculation -\useplength{refhpos}+\useplength{toaddhpos} does not result in a value, that moves the signature to the middle of the text area.
In your example the value of refhpos is 0pt and the value of toaddrhpos is -10mm (given by NF.lco). Your
\@setplength{sigindent}{-\useplength{refhpos}+\useplength{toaddrhpos}}
(I've remove one }, which was to much), would result in a sigindent of -10mm. This would result in a position 10mm left to the left edge of the text area. So it is not what you want.
The image you've linked (which is figure 22.1 of the current KOMA-Script manual), is about address fields at the left side. You are using an address field on the right side. So toaddrhpos is the distance from the right paper edge to the right address field edge. It is negative (as told above). The refhpos has nothing to do with the position of the address field.
Please have a look into table 22.1 in part II of the KOMA-Script manual and into the descriptions of the pseudo length in section 22.1 to see, how the values of toaddhpos, refhpos and sigindent are interpreted by scrlttr2.
You may try something like:
\setplength{sigindent}{.5\textwidth}
Or a more complicate but correct calculation:
\setplength{sigindent}{\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}+\useplength{toaddrindent}-\oddsidemargin-1in}
Note: This does only work for toaddrhpos < 0.
\paperwidth+\useplenth{toaddrhpos} is the position of the right edge of the address field relative to the left edge of the paper. Subtracting \useplength{toaddrwidth} results in the left edge of the address field relative to the left edge of the paper. Adding \useplength{toaddrindent} results in the left edge of the address relative to the left edge of the paper. But sigindent is relative to the left edge of the text area not the paper. So we have to subtract the left margin, which is (in oneside documents for all pages) \oddsidemargin+1in.
Note: Since KOMA-Script 3.26 \setplength instead of \@setplength is recommended. \@setplength is an internal command now. You should not longer use it. If you are using an outdated KOMA-Script release you still have to use \@setplength. But in this case also expressions in the second argument would not be allowed. So you would have to use:
\makeatletter
\@setplength{sigindent}{\dimexpr\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}+\useplength{toaddrindent}-\oddsidemargin-1in\relax}
\makeatother
or split the calculation into several \@addtoplength.
Here is an example (using KOMA-Script >= 3.26), that illustrates the calculation:
\documentclass[%
paper=a4,
fontsize=11pt,
french,
]{scrlttr2}[2018/12/22]% for KOMA-Script < v3.26 see the note about \setplengt` above
\usepackage{eso-pic,picture,xcolor}% for demonstration only
\usepackage{babel}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{hyperref}
%\LoadLetterOption{visualize}
%\showfields{head,foot,address,location,refline}
\LoadLetterOption{NF}
\renewcaptionname{french}{\subjectname}{Objet}
\renewcaptionname{french}{\ccname}{C.c.}
\KOMAoptions{
,foldmarks=false
,refline=nodate
,subject=titled
,fromemail=false
,fromlogo=false
,fromphone=false
,fromurl=false
,backaddress=false
,foldmarks=false
}
% from name
\setkomavar{fromname}{Chef Abraracoursix}
\setkomafont{fromname}{\scshape}
\setkomavar{signature}{\noindent Chef Abraracoursix,\\Un chef à toujours bras long.}
\setplength{sigindent}{\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}+\useplength{toaddrindent}-\oddsidemargin-1in}
% Show the calculation (for demonstration only)
\AddToShipoutPicture{%
\AtPageUpperLeft{%
\color{red}%
\footnotesize
\put(0,-\useplength{toaddrvpos}){%
\vector(1,0){\dimexpr\paperwidth+\useplength{toaddrhpos}\relax}%
}%
\put(0,-\useplength{toaddrvpos}){%
\makebox(\dimexpr\paperwidth+\useplength{toaddrhpos}\relax,\ht\strutbox)[cb]{\ttfamily\detokenize{\paperwidth+\useplength{toaddrhpos}}}%
}%
\color{red!80!blue!80}%
\put(\dimexpr\paperwidth+\useplength{toaddrhpos}\relax,-\dimexpr\useplength{toaddrvpos}+\ht\strutbox\relax){%
\vector(-1,0){\useplength{toaddrwidth}}%
}%
\put(\dimexpr\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}\relax,-\dimexpr\useplength{toaddrvpos}+\ht\strutbox\relax){%
\makebox(\useplength{toaddrwidth},\ht\strutbox)[cb]{\ttfamily\detokenize{\useplength{toaddrwidth}}}%
}%
\color{red!60!blue!60}%
\put(\dimexpr\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}\relax,-\dimexpr\useplength{toaddrvpos}+\ht\strutbox*2\relax){%
\vector(1,0){\useplength{toaddrindent}}%
}%
\put(\dimexpr\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}\relax,-\dimexpr\useplength{toaddrvpos}+\ht\strutbox*2\relax){%
\makebox(\useplength{toaddrindent},\ht\strutbox){%
\ttfamily\detokenize{\useplength{toaddrindent}}%
}%
}%
\color{green}%
\put(\dimexpr\oddsidemargin+1in\relax,
-\dimexpr\useplength{toaddrvpos}+2cm\relax){%
\vector(1,0){%
\dimexpr\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}+\useplength{toaddrindent}-\oddsidemargin-1in\relax
}%
}%
\put(\dimexpr\oddsidemargin+1in\relax,
-\dimexpr\useplength{toaddrvpos}+2cm\relax){%
\makebox(\dimexpr\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}+\useplength{toaddrindent}-\oddsidemargin-1in\relax,\ht\strutbox)[lb]{%
\detokenize{\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}+\useplength{toaddrindent}-\oddsidemargin-1in}%
}%
}%
\color{blue}%
\put(\dimexpr\paperwidth+\useplength{toaddrhpos}-\useplength{toaddrwidth}+\useplength{toaddrindent}\relax,0){%
\line(0,-1){\paperheight}%
}%
}%
}
% from adress
\setkomavar{fromaddress}{Place du village,\\Erqy,\\Armorique}
\setkomafont{fromaddress}{\small}
% place and location
\setkomavar{place}{Erqy}
\setkomavar{placeseparator}{, le }
% other komavar
\setkomavar{ccseparator}{}
\setkomavar*{ccseparator}{\llap{\ccname\quad}}
\date{\today}
% firsthead
\setkomavar{firsthead}{%
\usekomafont{fromaddress}%
\parbox[b]{\useplength{firstheadwidth}}{%
{\usekomafont{fromname}\usekomavar{fromname}}%
\hfill{%
\usekomafont{placeanddate}%
\ifkomavarempty{place}{}{\usekomavar{place}\usekomavar{placeseparator}}
\usekomavar{date}
}%
\\\usekomavar{fromaddress}%
\medskip
\if@phone\\\usekomavar*{fromphone}\usekomavar{fromphone}\fi%
\if@mobilephone\\\usekomavar*{frommobilephone}\usekomavar{frommobilephone}\fi%
\if@fax\\\usekomavar*{fromfax}\usekomavar{fromfax}\fi%
\if@email\\\usekomavar*{fromemail}\usekomavar{fromemail}\fi%
\if@www\\\usekomavar*{fromurl}\usekomavar{fromurl}\fi%
}%
}
\renewcommand*{\raggedsignature}{\raggedright}
\hypersetup{%
pdfauthor={Chef Abraracoursix},
pdftitle={Invitation pour une banquet au sanglier Roti},
pdfcreator={Emacs 26.1 (Org mode 9.1.9)},
pdflang={French}
}
\begin{document}
\setkomavar{subject}{Invitation pour une banquet au sanglier Roti}
\begin{letter}{%
Capitaine Paulus Romanicus\\
Camp de Babaorum
Bretany}
\opening{Le Romain,}
Dans le cadre des rapports de bon voisinage et de notre hospitalité
légendaire, nous vous invitons à festoyer avec nous sous le grand chêne,
du coucher du soleil à l'aube, à la prochaine plein lune pour le mariage
de la belle Fabala et de vigourix.
\closing{À la tienne !}
\end{letter}
\end{document}
Note, there were several other issues with your code:
\usepackage[francais]{babel}
is deprecated. Current babel warns:
Package francais.ldf Warning: Option `francais' for Babel is *deprecated*,
(francais.ldf) it might be removed sooner or later. Please
(francais.ldf) use `french' instead; reported on input line 31.
\KOMAoption{
,foldmarks=false
,refline=nodate
,subject=titled
,fromemail=false
,fromlogo=false
,fromphone=false
,fromurl=false
,backaddress=false
,foldmarks=false
}
is wrong. \KOMAoption has two arguments. The first one is an option key, the second is a list of option values.
To help users to find out what's wrong, the current prerelease of KOMA-Script shows the following error message with your wrong usage of \KOMAoption:
./test.tex:28: Package scrbase Error: syntax error in key ` ,foldmarks=false ,r
efline=nodate ,subject=titled ,fromemail=false ,fromlogo=false ,fromphone=false
,fromurl=false ,backaddress=false ,foldmarks=false '.
See the scrbase package documentation for explanation.
Type H <return> for immediate help.
...
l.28 }
You've used `\...Option' to set the key ` ,foldmarks=false ,refline=nodate ,sub
ject=titled ,fromemail=false ,fromlogo=false ,fromphone=false ,fromurl=false ,b
ackaddress=false ,foldmarks=false '
to new value(s), but `,' is not allowed in the key of an option
(and `\...Option' does not use `,' to separate several keys).
Maybe you've meant \...Options instead of \...Option.
If you'll continue, I'll give it a try, but you should expect further
and even strange error messages.
As the help text of the error message explains:
\KOMAoptions{
,foldmarks=false
,refline=nodate
,subject=titled
,fromemail=false
,fromlogo=false
,fromphone=false
,fromurl=false
,backaddress=false
,foldmarks=false
}
would be correct.
Your definition of firsthead adds several significant but unwanted white spaces. See What is the use of percent signs (%) at the end of lines? for more information how to avoid them.
There is also a warning message about usage of \date:
Class scrlttr2 Warning: \date changes the internal \LaTeX date only.
(scrlttr2) You should note that this changes the default
(scrlttr2) value of variable `date' only as long as someone
(scrlttr2) uses `\setkomavar` to change the content of
(scrlttr2) variable `date'.
(scrlttr2) Therefore, usage of `\setkomavar' is recommended
(scrlttr2) to change the letter's date on input line 59.
So for scrlttr2 you should use
\setkomavar{date}{\today}
or just remove it, because \today is already the default.
Last but not least, you have a
makeatletter
instead of
\makeatletter
in your document preamble.
refhposis 0pt in your example and must not be used for the calculation.