Pillowcase, I have just one kid, in Y2 in England, only just 7 and she only has very very basic French. She is doing a French club at school and can conduct extremely basic conversations and she and I do a little practice most days at remembering words and having little conversations. Work wouldn't be a problem. DH is very freelance and all over the country and Europe with his jobs, and DD and I hardly see him anyway. Being in France would just add a day either side of his jobs and we'd just see him for four days less a month. The rent on renting our house out here would cover the small remaining mortgage on our London house and probably pay for our rent in the Gers if we rented fairly modestly (but worst case DH could cover rent and mortgage and bills if we ate plenty of lentils etc). DH could never work in France. He just hasn't got the language skills for his v specialised job and I am not convinced he could acquire them. I currently have a job I could do remotely but one of the reasons for thinking of moving is that I think it might disappear soon. I may get a reasonable redundancy payment, too, which would be a useful thing.
I think we would do it for a year as an experiment and see how it went. If it didn't go well, we'd have lost nothing and DD would have gained some valuable language skills. If it did go well, we'd reassess in a year and see what we felt (including the views of DD who is currently half in love with the idea and half terrified - these are also my feelings).
I absolutely wouldn't buy anywhere unless definite on a long-term plan. My aunt has been half-thinking of selling her house in the local area for some years now and has received some really quite low valuations!
Did your son win against Estang? I have to tell you, I'm rooting for Estang here, because my friend up the road from where we stay runs the local butcher (the old one, not the new one) and there's a man in the car park by the restaurant who sells me lovely strawberries from his garden even though he is a bit ancient and I think he ought to be having a bit of a rest.
My main worry is DD and school, really. She's an only so would be initially a bit isolated (though if I wasn't working I would have more time to be with her). But she is a child who positively loves being sat down and told to do things so might not mind the French education system too much....
What an essay!