\documentclass[11pt,twoside]{letter}
\pagenumbering{gobble}

\usepackage{lmodern}
\usepackage{carlletter}

\usepackage{graphicx}
\graphicspath{{img/}}

\usepackage[autostyle]{csquotes}
\MakeOuterQuote{"}

\begin{document}

    Vincent Lannurien \\
    64 rue Paul Masson \\
    29200 Brest
    
    \begin{flushright}
        À l'attention de ...
    \end{flushright}
    
    \begin{flushright}
        le , à, \\
    \end{flushright}

    \vspace{40px}
    
    Madame, Monsieur,

    \vspace{20px}

    ...

    \vspace{40px}
    
    \begin{flushright}
        Vincent Lannurien

        \vspace{20px}
        
        \includegraphics[width=4cm]{signature.png}
    \end{flushright}
\end{document}