If you need broadband at home, you have the following options - 4 or 5G service from a cellphone provider (some are offering unlimited data), traditional landline as that still has the best geographical coverage or Vrigin Media if they are in your neighbourhood. There are smaller providers like HyperOptic but they are mostly present in places like London as they prefer to wire up large apartment buildings. By the way, the cheapest service is also the slowest at around 10 Mbps. If you have more than 1-2 devices streaming simultaneously, this may not be enough. A great site for UK related deals is hotukdeals.com which will help you find some cheap plans (as also moneysavingexpert.com) - I don't have any stake in these sites apart from being a satisfied user.

For calling within the family, is WhatsApp a serious option given that almost everyone now has at least a basic smartphone? That will eliminate the need for a French number. As for Brexit related roaming, different service providers have taken a different commercial stance, so you will have to check separately.