I'm in France, I used GP since that's the term that seems to be used in the Anglosphere. It also seems like a reasonable translation of the French term – médecin généraliste.
I'm hearing bad things about UK's NHS, and while I don't have any firsthand experience with it, I do get the feeling that the French system is going down the same path.
It's true that I don't usually think about going the private route. I'm not 100% sure, but I think you can probably see a private specialist directly. I also don't know how much it would cost, but probably quite a lot, given the prices in the public hospitals, and I don't think it's covered by the insurance, even though I carry insurance above the standard national scheme.
I was actually in France last year, and arrived having lost (in transit; baggage handlers) some medicine for my son which had been prescribed in the UK by our GP the previous day, as he'd had stomach symptoms.
I contacted the local French doctor, who brought us in that day, gave my son an actual examination (the UK GP didn't do this), asked if I was aware that he had an ear infection (I wasn't, the UK doctor didn't check), and revised the course of treatment which resolved the problem quickly.
I was extremely impressed by the French doctor; he was in a different league to the standard in the UK.
I'm hearing bad things about UK's NHS, and while I don't have any firsthand experience with it, I do get the feeling that the French system is going down the same path.
It's true that I don't usually think about going the private route. I'm not 100% sure, but I think you can probably see a private specialist directly. I also don't know how much it would cost, but probably quite a lot, given the prices in the public hospitals, and I don't think it's covered by the insurance, even though I carry insurance above the standard national scheme.