I do some work but it's all for anglophone readers - and you have to be great at writing AmE as well as BrE. I write for DIY/Interior/Craft mags in the US and educational fields as well as occasionally for craft/DIY/Interior in the UK - I used to work for the MEN.
You might find some work for English publications based in France, but the pay is not good.
Mentioning no names, but I had a 'trial' (i.e. I spent four days!) with an English monthly over here who wanted me to do all my own research, be fluent in both English and French and write to a non-existent house style that they couldn't explain, but they knew existed. I didn't get paid and even if I had been paid, they were offering a salary for a full time position, 6 days a week, of 800€ a month. That's for a Masters in writing, fluency in French - and they wanted SEO experience to boot. Luckily, being 20 years in the world of writing kind of gives you that, but I was unprepared for their appalling attitude. They didn't even have the courtesy to tell me I got it or didn't get it, or even give me thanks, even though I did almost a week's worth of work for them for nothing!
I would ask though if you decide to go down the teaching route, please get a teaching qualification of some kind. Just because you use language and are qualified with language doesn't mean you are with teaching. In fact, the teaching side is more important to me than the language side! Depending on where you are, there are vast tracts of France where you can't command a respectable salary unless you live near a city. The department I work in has a bigger area than Lancashire and fewer people than Coventry... Skype lessons are the way forward! It took 18 months before business started to come in, though.
If you plan on teaching English in a French school, a PGCE is pointless - sorry, Andrew! University of Poitiers/Limoges/Bordeaux won't accept it above the CAPES. You'd need to take the CAPES. You could find work in schools as an assistant - but you're virtually a teacher without the pay or the position. As it is right now, they'd prefer a French speaker who teaches French children to say 'bruzzere' and 'muzzere' and even writes that this is how it is said. It's similar in England - most MFL teachers in the UK are English - you might find 1 in 5 who are native, but then they are co-opted to teach Spanish or German as well.
You could find lots of work writing copy for online copy businesses - they're finally coming back round to the fact that yes they can find a cheaper article from India, but realise that it's a different type of English than BrE or AmE. I don't do it full time, but it's certainly filled the gaps between paychecks! That's quite interesting and varied business and the more experience you have, the better. You could be writing about the Brazilian parliament one day and about shoes on the catwalk the next. It's not well-paid at first, but you can live anywhere and the more you do, the more you command.
Pessimistic and cynical, I know, but then the world also changes very quickly (although France doesn't)! And virtual journalism is on the up-and-up, especially if you are a niche specialist. What you need there, though, is niche first and then journalism experience. If it's a quirky niche, with a British background and living in France, the American readers will love you. It must be said, these niches are creative, by and large. David Lebowitz is a good example (he's American though).
And another thing, if you want to write and you haven't already, get a blog. There are lots of great blogs out there that are well-run and well-presented. If you blog in French, in a niche, you'll get the attention of French magazines quite quickly, since proportionally, France isn't all that 'bloggy' yet. If you blog in English, you can very quickly work your way up to magazine features, guest blogging, and then books! Again, niche is more important than journalism - though being good at writing is an obvious bonus, as is being good at photography. Regular, interesting, lively and personal content on a theme is usually a quick recipe for success; it acts as a virtual portfolio and I'd guess 50% of my new work comes via my blogs/website.
Epic response! Hope it's of some help. Feel free to contact me if you want any more info.