test.tex

\documentclass[fancytabs,8pt,pagesize=pdftex,paper=a5]{diary}

\usepackage[french]{babel}
%\usepackage{moredatetime}
%\let\diaryformatdate\formatdateny
\usepackage{lipsum}

\begin{document}

\begin{diary}
\diarymonth

\diaryday{First day}

\lipsum

\diaryday{Another day}

\lipsum

\diaryday{A third day}

\lipsum

\diarymonth

\diaryday{First day of second month}

\lipsum


\end{diary}

\end{document}