I don't mean to be glib, but a week of aftercare in the hospital is not what every woman wants. I was much happier being home while my husband was caring for the baby. Hospitals are not generally fun places even if it comes with childcare. I trust my husband with a baby far more than the hospital staff, especially during covid where visitor hours are restricted.

First congratulations. I moved here from UK 9 years ago and was more or less in the same situation as you with permit and insurance. I joined my partner but we already had 2 kids. He had B permit and I received also B, but it took few months to come.
Talking about insurance, I took free choice of family doctor model, as I didn’t speak any French and didn’t want to call first some call centre or whatever. This model works for us. If needed I just go any GP that is on duty.
For gynaecologist, optician and Pediatra you don’t need a referral in this model .
Franchise 2500ch , had it for 8 years. Dropped it last year.
Pregnant with third kid 8 years ago. For antenatal classes look at your gynaecolog place, mine (in Rolle) had plenty leaflets. All questions about pregnancy talk with your gynaecologist because here until end he will look after your pregnancy, not midwife as it is in UK. Midwife you will need for after birth, so she will come to home to check on you and the baby. I got the list from hospital de Morges, whee I gave birth. You should try to find one a bit earlier, because they tend to be quite busy and not always easy to find one and speaking English.
If you need GP check centre medical de morges at rue de la gare. They wee still taking new patients.
You will need to find a Pediatra for a baby too, don’t leave it for the last minute.