Your first issue : write month in French it’s not an ACF issue but a PHP one because you use ‘DateTime()‘ an ‘format‘ and this only works in English. If you want to get the month in French you can :
For the first solution, the exemple :
Traduce_Month = array ( "January" => 'Janvier', "February" => 'Fevrier', ... ) echo '<h4 class="blanc">' .Traduce_Month[$monthKey]. ' ' . $yearKey . '</h4>';
For the second one you can find all the documentation needed in PHP codex by searching ‘strftime‘ and ‘DateTime::createFromFormat‘ (to convert you date).
For your second issue (still a PHP issue), to write the event date you just have to get the $date value you saved in your array ‘$group_posts[$year][$month]‘ and echo it by using ‘$date->format‘ as you already done.
Hope it’s help
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