Add initial of the author with biblatex (footcite)

Question

I use \footcite command. The first time a key is used, I obtain the full reference but the second time, I obtain a short version. The trouble is that in the short version I want to have initial of the author and currently I haven't.

MWE:

\documentclass{article} 
\listfiles
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@ARTICLE{article,
  author = {Nachname, Vorname},
  title = {Titel des Zeitschriftenartikels},
  journal = {Zeitschrift},
  year = {2006},
  volume = {6},
  translator = {Talu, Jean},
  pages = {19--75}
}
@BOOK{book,
  author = {Buchautor, Hans-Wilhelm},
  title = {Irgendein Buch},
  address = {Buch am Wald},
  year = {2000}
}
\end{filecontents}


\usepackage[main=french,ngerman,english]{babel}




%bibliographie
\usepackage[
bibstyle=verbose,
citestyle=verbose-ibid,
autocite=footnote, 
language=french]{biblatex}
\bibliography{\jobname} 


\begin{document}
\cite{book}
\cite{article}
\newpage
\autocite{article}
\autocite{article}
\newpage
\autocite{article}
\newpage
\printbibliography

\end{document}

Answer 1

You could redefine verbose's cite:short with:

\renewbibmacro*{cite:short}{%
  \printnames[mygiveninit-family]{labelname}%
  \setunit*{\printdelim{nametitledelim}}%
  \printtext[bibhyperlink]{%
    \printfield[citetitle]{labeltitle}}}

That supposes a defined name format mygiveninit-family which can be defined as (I don't think there is a name format which prints initials irrespective of the global option giveninits, so I defined one, assuming you don't want to tamper with the option):

\DeclareNameFormat{mygiveninit-family}{%
    \usebibmacro{name:given-family}
      {\namepartfamily}
      {\namepartgiveni}
      {\namepartprefix}
      {\namepartsuffix}%
    \usebibmacro{name:andothers}}

A full working example:

\documentclass{article} 

\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@ARTICLE{article,
  author = {Nachname, Vorname},
  title = {Titel des Zeitschriftenartikels},
  journal = {Zeitschrift},
  year = {2006},
  volume = {6},
  translator = {Talu, Jean},
  pages = {19--75}
}
@BOOK{book,
  author = {Buchautor, Hans-Wilhelm},
  title = {Irgendein Buch},
  address = {Buch am Wald},
  year = {2000}
}
\end{filecontents}

\usepackage[main=french,ngerman,english]{babel}

%bibliographie
\usepackage[
bibstyle=verbose,
citestyle=verbose-ibid,
autocite=footnote, 
language=french]{biblatex}
\addbibresource{\jobname.bib} 


\renewbibmacro*{cite:short}{%
  \printnames[mygiveninit-family]{labelname}%
  \setunit*{\printdelim{nametitledelim}}%
  \printtext[bibhyperlink]{%
    \printfield[citetitle]{labeltitle}}}

\DeclareNameFormat{mygiveninit-family}{%
    \usebibmacro{name:given-family}
      {\namepartfamily}
      {\namepartgiveni}
      {\namepartprefix}
      {\namepartsuffix}%
    \usebibmacro{name:andothers}}

\begin{document}
\cite{book}
\cite{article}
\newpage
\autocite{article}
\autocite{article}
\newpage
\autocite{article}
\newpage
\printbibliography

\end{document}

Which will produce this short citation: