This is not exactly what your professor seems to want, but it might be close enough
\documentclass[french]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=authoryear, backend=biber, citetracker]{biblatex}
\addbibresource{biblatex-examples.bib}
\newbibmacro{fullcite}{%
\usedriver
{\DeclareNameAlias{sortname}{default}}
{\thefield{entrytype}}}
\DeclareFieldFormat{footnote}{\mkbibfootnote{#1}}
\DeclareCiteCommand{\ffparencite}[\mkbibparens]
{\usebibmacro{prenote}}%
{\usebibmacro{citeindex}%
\usebibmacro{cite}%
\ifciteseen
{}
{\printtext[footnote]{\usebibmacro{fullcite}}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\DeclareMultiCiteCommand{\ffparencites}[\mkbibparens]{\ffparencite}{\multicitedelim}
\DeclareAutoCiteCommand{inlineff}{\ffparencite}{\ffparencites}
\ExecuteBibliographyOptions{autocite=inlineff}
\DeclareDelimFormat{nameyeardelim}{\addcomma\space}
\DefineBibliographyExtras{french}{\restorecommand\mkbibnamefamily}
\begin{document}
\autocite{sigfridsson} and \autocite{sigfridsson}
\autocite{nussbaum,geer}
\printbibliography
\end{document}
The code automatically adds a footnote with the full reference on the first citation. The footnote is inside the brackets to give reasonable output for the case \autocite{nussbaum,geer}.

Alternatively,
\documentclass[french]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=authoryear, backend=biber, citetracker]{biblatex}
\addbibresource{biblatex-examples.bib}
\makeatletter
\newcommand*{\ffparenwrap}[1]{%
\undef\blx@ffcite
\mkbibparens{#1}%
\ifundef\blx@ffcite
{}
{\footfullcite{\blx@ffcite}}%
}
\DeclareCiteCommand{\ffparencite}[\ffparenwrap]
{\usebibmacro{prenote}}%
{\usebibmacro{citeindex}%
\usebibmacro{cite}%
\ifciteseen
{}
{\ifundef\blx@ffcite
{\xdef\blx@ffcite{\thefield{entrykey}}}
{\xappto\blx@ffcite{,\thefield{entrykey}}}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\makeatother
\DeclareMultiCiteCommand{\ffparencites}[\mkbibparens]{\ffparencite}{\multicitedelim}
\DeclareAutoCiteCommand{inlineff}{\ffparencite}{\ffparencites}
\ExecuteBibliographyOptions{autocite=inlineff}
\DeclareDelimFormat{nameyeardelim}{\addcomma\space}
\DefineBibliographyExtras{french}{\restorecommand\mkbibnamefamily}
\begin{document}
\autocite{sigfridsson} and \autocite{sigfridsson}
\autocite{nussbaum,geer}
\printbibliography
\end{document}
makes sure that the footnote comes outside the round brackets. But it has to coerce several citations into one footnote to achieve this.

If you change \makeatletter...\makeatother block to
\makeatletter
\newcommand*{\ffparenwrap}[1]{%
\let\blx@ffcite\@empty
\mkbibparens{#1}%
\ifdefvoid\blx@ffcite
{}
{\forlistloop{\footfullcite}{\blx@ffcite}}%
}
\DeclareCiteCommand{\ffparencite}[\ffparenwrap]
{\usebibmacro{prenote}}%
{\usebibmacro{citeindex}%
\usebibmacro{cite}%
\ifciteseen
{}
{\listxadd\blx@ffcite{\thefield{entrykey}}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\makeatother
the citations get a footnote each at the expense of possibly clashing footnotes.
biblatexis probably your best choice. You are not usingbiblatexat the moment, so while you are waiting for an answer you may want to check out how to getbiblatexto work with LyX. LyX 2.3 (released this spring) has massively improved support forbiblatex, so if you can upgrade, you may want to consider doing that (as always upgrades or updates shortly before a deadline can be ill-advised, you never know what breaks). For older versions of LyX you can have a look at https://tex.stackexchange.com/q/298382/35864. For LyX 2.3 see https://wiki.lyx.org/BibTeX/Biblatex – moewe Jul 18 '18 at 14:03(AUTHOR 2018)(with weird kerning) and I'm aiming for(Author, 2018). – n49o7 Jul 18 '18 at 15:01\DefineBibliographyExtras{french}{\restorecommand\mkbibnamefamily}produces an error when placed in the preamble. MNWE : https://pastebin.com/raw/cjWJ1G9X -- I was able to get a comma by usingBiblatex (natbib mode)as style format. – n49o7 Jul 18 '18 at 15:20biblatexversion is outdated. – moewe Jul 18 '18 at 15:21upon parsing the command, and cascading errors from there. Apparently I'm usingBiblatex 3.11, even-though I ran MikTex update before updating toLyX 2.3`, so that could very well be it. I'll sort it out. In the meantime your answer is pretty good. I'll still post mine. – n49o7 Jul 18 '18 at 15:51biblatex3.11 is the current version. So that can't be it. Can you cite which command exactly is supposed to be undefined? – moewe Jul 18 '18 at 15:52biblatex. Andbiblatexis only loaded right before\begin{document}. Can you somehow tell LyX to move the\DefineBibliographyExtras{french}{\restorecommand\mkbibnamefamily}to after\usepackage{biblatex}? – moewe Jul 18 '18 at 15:59biblatex. But indeed I think this is something you should raise in a LyX forum regardless. If there is non good way, you may want to phrase this is a a feature request. It really is crucial forbiblatex's customisability to be able to insert code in the preamble afterbiblatexis loaded. And no, I don't think this is the longest comment thread, they often have the tendency to grow uncontrollably when I get involved ;-) – moewe Jul 18 '18 at 16:13biblatexin the preamble, and you can put whatever you want before it and after it. – scottkosty Jul 19 '18 at 07:38\DefineBibliographyExtras{french}{\restorecommand\mkbibnamefamily}is still in the preamble, when it should be between the end of the preamble and the beginning of the document. – n49o7 Jul 19 '18 at 13:15