\documentclass{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
 
\usepackage[french,german,english]{babel}
\usepackage[babel=true]{csquotes}

%\MakeForeignQuote{german}{<}{>}

\begin{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Quoting in Current Language}

\selectlanguage{french}
\subsection{\languagename}
\enquote{Citation extérieure}
\enquote{Extérieure \enquote{intérieur} extérieure}

\selectlanguage{german}
\subsection{\languagename}
\enquote{Äußeres Zitat}
\enquote{Äußeres \enquote{inneres} Äußeres}

\selectlanguage{english}
\subsection{\languagename}
\enquote{Outer Quote}
\enquote{Outer \enquote{Inner} Outer}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Quoting in Foreign Language}

\subsection{french}
\foreignquote{french}{Citation extérieure}
\foreignquote{french}{Extérieure \foreignquote{french}{intérieur} extérieure}
\foreignquote{french}{Extérieure \foreignquote*{french}{intérieur} extérieure}

%\subsection{Auto Quote German}
%< Äußeres Zitat >

\subsection{german}
\foreignquote{german}{Äußeres Zitat}
\foreignquote{german}{Äußeres \foreignquote{german}{inneres} Äußeres}
\foreignquote{german}{Äußeres \foreignquote*{german}{inneres} Äußeres}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{textquote in Current Language}

\selectlanguage{french}
\subsection{\languagename}
\textquote[Citation]{du texte ici}

\selectlanguage{german}
\subsection{\languagename}
\textquote[Zitat]{etwas Text hier}

\selectlanguage{english}
\subsection{\languagename}
\textquote[Citation]{some text here}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{textquote in foreign Language}

\foreigntextquote{french}[Citation]{du texte ici}
\foreigntextquote{german}[Zitat]{etwas Text hier}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{displayquote in Current language}

\selectlanguage{french}
\subsection{\languagename}
\begin{displayquote}[Citation]
du texte ici
\end{displayquote}

\selectlanguage{german}
\subsection{\languagename}
\begin{displayquote}[Zitat]
etwas Text hier
\end{displayquote}

\selectlanguage{english}
\subsection{\languagename}
\begin{displayquote}[Citation]
some text here
\end{displayquote}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{displayquote in foreign Language}

\begin{foreigndisplayquote}{french}[Citation]
du texte ici
\end{foreigndisplayquote}

\begin{foreigndisplayquote}{german}[Zitat]
etwas Text hier
\end{foreigndisplayquote}

\end{document}