As it seems to be there is a big cultural clash going on regarding expectations of visiting, time spent together and so on, is it worth having a very general conversation with him around what happened when he was little - were his GPs around a lot, any differences between the way that his mother and father's sides of the family were treated, how that related to what his friends experienced, what the general expectations are that he's grown up with and takes as normal...
Then move on to finding out what he thinks you grew up with - how often he thinks that you would have seen your GP and what you think is normal, what your general expectations are of what people in your situation would normally do.
Double check that he hasn't managed to rationalise any particular quirks - eg if you didn't see some GP very often because they lived a long way away, then he might just assume that you would have seen them more but couldn't because it was too expensive or that the travelling time didn't work when you had school/parents had to work. Or that he thinks that they didn't care so didn't bother but that this was 'abnormal' and that your friends would have spent similar amounts of time to him with GPs. Or whatever.
You never know - you might discover that his parents figure that as your parents are so far away they see it as their duty to come even more often so that your dc gets to see a grandparent at least every month or they see it as an opportunity to come even more and so on.
Hopefully the conversation will throw up that you both have very different experiences and expectations of what being a parent involves and how grandparents fit into the picture. Make sure that you emphasize that this doesn't make either version right or wrong, they're just different and that's fine. But that it does mean you need to actively find a compromise rather than for him to assume that you will neatly slot into his expectations or vice versa.
You also need to go back and talk about how you felt in light of this when his mum came to stay previously - it's not going to be easy unfortunately but hopefully if you couch it in terms of 'when she did xxx I felt yyy' rather than 'she did xxx wrong' which is going to put his back up (rightly or wrongly!) and put him on the defensive of his mum. And then go on to say that the cumulative effect of feeling yyy and yyy and yyy and [insert as many examples as you have] was that you felt undermined, unable to bond with your child, pushed out, and so on, to the point that you would have preferred to have been in pain and without her there. That you put up with it for a long time because you love your dh but you also feel upset that he cared more about his mum and her expectations than he did about you and your feelings at a time when you were feeling very vulnerable and could have done with his total support. If you're using words like bully and torture to describe her behaviour towards you then he has to know otherwise he is never going to understand why you have such a problem now because in his mind when you said she could go home because you were well enough to cope, you didn't put up a fight and so probably wanted her to stay longer (It's easy to rationalise things that you want to happen - ie you want your mum to stay longer, your dp says she can go home, but as she doesn't really protest hard then she was probably just being thoughtful towards your mum and was actually really happy to have her help out for longer)
Say that as you've had to endure seven weeks of having somebody there, you need at least that of having nobody there to get yourself back on an even keel. And that you're not prepared to commit to a regular visiting schedule beyond that, you'll agree to a single visit initially from each parent, see how it goes and then take it from there. If they behave all goes well, then you can arrange the next visit in a couple of months time. If not, you'll wait longer until the next visit is arranged.
It sounds like you get on better with your FIL than your MIL so would it be worth suggesting that FIL is your first visitor of the two of them - it won't be so terrifying to think of it happening, see what happens and what works well, what doesn't and use that info to help when deciding on a date for your mil to come.
And finally - if your dh keeps on saying that you ought to move to France, just keep saying (even if you don't mean it) that you've been thinking and that because of the way the visits have made you feel so far, you think that actually you'd all be much better off moving back to the USA again, that you think you'd all be much happier there. There's no way he's going to want that - so at least that might get you to stay in England with more reasonable visits vs moving to france! It will also remind him that you're a partnership - and that as equal partners you get to compromise, he doesn't get to make all the decisions!