Well I’m a professional photographer, although I am still based in the UK rather than France… however I know a couple of colleagues who successfully made the move from UK to France as freelance (wedding) photographers, one before Brexit and the other during Covid!
Fortunately photography is not one of those professions where any French qualifications are required - as an EU citizen you can set up as self-employed and offer your services. As you mentioned it would take some time to find clients and build the business, but that will apply to any self-employed activity.
One of my friends (who lives near Bèziers) continued to shoot weddings in the UK while building up her French business, thanks to Ryanair (!) so that might be an option if you have photo clients in the UK! (The other friend had already planned to move to France before Brexit arose so had been shooting destination weddings in France as his main business for a number of years, travelling from the UK).
Teaching I believe does need recognised qualifications but others can advise you on that.
What kind of photography do you do? I think shooting destination weddings for UK/US clients would be quite possible in the South of France, if that’s of interest. My friend also does some property photography I think.