Do what you want, as others have said, but also consider whether doing so would make life easier - for them or for you. The trade-off is how often it’s read and mispronounced by strangers vs. how often it’s written and misspelled by strangers.

You said it’s French; for example, if it’s “Jean” then the “correct” pronunciation would sound like “zhawn”. This might cause many native English speakers to mishear it as “John”. “Michel” sounds like “Michelle”.

On the other hand, they might read Jean and say “Gene” or see “Michel” and say “Michael”.