There is a Parents in France group on FB which might help with some of your questions.
Schools are easy: you either attend your catchment school or go private (bit more complicated than this in big cities, but this is the general rule). Your catchment school is obliged to find room for your child. Private schools may have waiting lists, depends hugely on the area. (Note that private school in France is not really private - more like a UK church school with minimal fees which are often means tested.)
Internet/telephone is just a question of choosing one of the operators and then waiting for them to connect you. They are all a bit rubbish but on the whole you get better services for less money than in the UK (40€-ish a month should get you fast internet, free calls to most countries and TV).
Food shops - depends where you live, as not all the chains are represented equally throughout France. Outside cities, on-line food shopping with home delivery is not well-developed, though "drive" operations where you order on-line then collect are spreading. We shop at Lidl for our main shop, Intermarché drive for top-ups, market for veg.
Clothes shops - lots of international brands on the high street - H&M, Mango, Zara. Depends where you live.
GP - once you are in the social security system you find a local GP who is willing to take you on. You have to declare your chosen GP to your insurer ("caisse") as not doing so reduces your reimbursements.