I am in France aswell just 2 hours south of paris. Where abouts are you? be great to touch base and chat more about being a pregnant mum in France as its very different if you dont have the support network around you.
Anyway congrats! Here is my 2 pennies...
I had a crap local Doctor so jumped the process and contacted the Hospital direct (the same hosptail I plan to have the baby in.)
You need to book your 12 week Scan ASAP. I booked mine at 6 weeks and only just got an appointment at the 12.5 week stage. Be warned a lot of hospitals here to the nuchal scan which could mean a vaginal scan (doesnt hurt at all!)
You then see your Gyne monthly (mine is at the same hospital). I had all my appointments booked up at 8 weeks pregnant.
At 15 weeks you will probably be told (and given a prescription) by your Gyne for full bloods and Urine tests. The best thing about france is that results go to the Doctor in 24 hours, so you dont have long to wait if there are any concerns. The Gyne will call you if he has issues with the results.
You then have scans like the UK at 20 weeks (can detemine sex of baby) and 30-32 weeks. Again all mine were booked when I went for my 12 week scan. In fact I have to go to a private clinic for the 20 week one as the hospital were fully booked!
At 5 or 6 months you may be invited by the hospital for a tour (each region differs) this will then allow you to see the rooms and birthing. You get to chat to the midwife one on one to talk about birthing options. You then have at least 1 antenatal class before this.
I really recommend you read Wendys blog here as if you are doing this on the french healthy system it helps you understand the paperwork. Luckily we are doing this on private insurance so jut a case of paying when we go and claiming back. having-a-baby-in-france.blogspot.com/
I have to say my experience of the GYNE and Doctors here to date has been fantastic. Hospitals look after you even if you have to wait based on delays and they are very thorough. Be warned you will get physical examinations at every Gyne visit, you get used to having your legs open very early on!