Following lockstep's request, here is my comment as an answer. Credit due entirely to Joseph.
Be warned that if you want to use footnotes that are not citations, you're going to run into some problems. Joseph recommends bigfoot
, but a commenter mentioned that this package has some issues with bugs, compatibility and ongoing support. This problem is examined further in another question.
\documentclass{scrbook}
\usepackage[french]{babel}
\usepackage[colorlinks=true]{hyperref}
\usepackage[style=chem-acs,hyperref=true,babel=hyphen]{biblatex}
\ExecuteBibliographyOptions{citetracker=true,sorting=none}
% No brackets around the number of each bibliography entry
\DeclareFieldFormat{labelnumberwidth}{#1\addperiod}
%---------------------------------------------------------------
% Essentially verbatim from Joseph Wright
% http://www.texdev.net/2010/03/08/biblatex-numbered-citations-as-footnotes/
\makeatletter
\let\cbx@citehook=\empty
\DeclareCiteCommand{\sfcite}[\cbx@superscript]%
{\usebibmacro{cite:init}%
\let\multicitedelim=\supercitedelim
\iffieldundef{prenote}
{}
{\BibliographyWarning{Ignoring prenote argument}}%
\iffieldundef{postnote}
{}
{\BibliographyWarning{Ignoring postnote argument}}}
{\usebibmacro{citeindex}%
\usebibmacro{sfcite}%
\usebibmacro{cite:comp}}
{}
{\usebibmacro{cite:dump}}
\newbibmacro*{sfcite}{%
\ifciteseen
{}
{\xappto\cbx@citehook{%
\noexpand\footnotetext[\thefield{labelnumber}]{%
\fullcite{\thefield{entrykey}}\addperiod}}}}
\newrobustcmd{\cbx@superscript}[1]{%
\mkbibsuperscript{#1}%
\cbx@citehook
\global\let\cbx@citehook=\empty}
\makeatother
%---------------------------------------------------------------
\bibliography{biblatex-examples}
\begin{document}
\chapter{Title}
\null\vfill\noindent
First citation.\sfcite[cf.][461]{companion}
First citation.\sfcite[e.g.][2589]{bertram}
Second ``multi'' citation.\sfcite{bertram,companion}
\printbibliography
\end{document}

Some notes:
- Citation links take you to the bibliography entry, not the footnote. This appears to deviate from a feature you requested in a previous question.
- I've dropped the entry number brackets in the bibliography to conform with your thesis example. A few other changes to this end could be made (e.g. author names in normal font instead of small caps and footnote numbers in superscript), but I personally wouldn't see these as improvements in typographic style.
bibstyle=chem-acs
andcitestyle=numeric-comp
.