Hello,
I am writing a letter to the family I will be staying with in France in October.
I wanted to say "Thank you for offering to have me/look after me"
I thought maybe: Merci à vous d'offrir m'avoir/ me garder.
"To have me" / "to look after me" sound good in English, but don't translate directly into French. I would say: Merci à vous de votre offre d'hébergement, or Merci à vous d'avoir proposé de m'héberger.