35-38 nights...France or UK ?

Reach in your pocket, grab a coin and flip heads or tails ... of all your pros and cons, my biggest take-away is possible summer heat waves, especially France ... my wife with my youngest daughter went to one of her high school friends wedding outside of Le Mans several years ago during their record setting (at that time) heat wave ... stayed in this awesome chateau, but no a/c ... totally miserable, they had to take 3-4 showers a day to try and cool off ... 10 minutes after the shower, they were sweat-soaked again ... I think that possibility alone would make me choose England / Scotland where the potential for a heat wave is smaller.

Go to France. If a heat wave comes to where you are staying, head to Brittany or Normandy.

UK(-) More expensive, Food ?

Yes the UK has food and lots of it. What you'll find in the UK is that there is a far greater variety of cuisines than what's available in France. In my opinion French food doesn't really warrant the high recognition that it receives and I think you can eat better and with a wider array of choices in the UK. When I was last in the south of France I eventually became bored of the food choices, pretty much every French cuisine restaurant was serving the same thing albeit with a few variations.

As for being more expensive, as a tourist you'll likely notice little difference between the two countries. There are far, far more museums with free entry in the UK as the British taxpayer funds the entrance fees even to non tax paying tourists. Groceries are cheaper in the UK with the exception of wine, the French win hands down on that one.

Both countries experience summer heatwaves however the temperature in the south and mid areas of France are typically higher than those experienced in the UK. Brittany and Normandy share a similar climate to England including heatwave temperatures.

I think your children would prefer the UK.

I adore both destinations. Given that you speak French and already have the trip planned out, that argues heavily for France in my book. However, I have a low tolerance for heat, so that would push me to Britain. Of course they have had very hot weather recently too, at least in southern England.

The key questions are: Can you tolerate heat? Can you fine accommodations with AC?

With the number of days you have, you could easily take in 2 countries.

We went from Madrid to Granada to Barcelona. And then we took the 6.5 hour, 650 mile fast train to Paris.

We found Spain to be very easy to travel in and substantially cheaper than France or the U.K. Inflation is raising its head in Europe, and France or the U.K. could easily be unbearably expensive for a family for a month.

Given basically 5.5 consecutive weeks to spend in one of the two countries, I choose France, a most auspicious opportunity to see again not just Paris but where ever without the time pressure. All the more so since you are quite comfortable in the language....fantastic. The only place I've spent 5 consecutive weeks was traveling and exploring cities/towns in Germany.

You won't have to be too concerned with the heat in Brittany in the summer, reputedly the coldest area of France in the summer relative to all other regions. True, that the heat waves in France have become more acute.

Likewise, for various reasons, I had to postpone my trip. The plan now is to get back to Paris and France the summer of 2023.

Both countries are great destinations.

We have traveled all over both Great Britain and France. While I find the people are nice in both, since I don't speak French, occasionally, I have encountered some rude Parisians. However, I had a French friend that was not from Paris and he said Parisian waiters were rude to him as well.

Both countries are diverse.
France has Paris, Normandy, Alsace, Burgundy, Provence, the Loire Valley, Bordeaux and more.
Britain has London, the English countryside, Wales, Scotland and N. Ireland.

You can find very scenic places in both. Both have cosine that is excellent. Britain once had a poor reputation in that area, but no more, due to diverse choices of Italian, Indian, French, and yes, British. Fish and Chips are wonderful and love English breakfasts and meat pies.
France has great cuisine and many choices. Love Croissants.

Renting a car in the UK is no problem, even driving on the left, since British drivers tend to be very polite. The French are OK in that area as well.

We did a wonderful four week driving tour of England and S. Wales. Here is my review with details.
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139

"What you'll find in the UK is that there is a far greater variety of cuisines than what's available in France. In my opinion French food doesn't really warrant the high recognition that it receives and I think you can eat better and with a wider array of choices in the UK."

I agree food in UK is better than its reputation and at the end it is ones personal taste anyway. But please forgive me that I had to smile. In my personal opinion hardly any chance that UK is beating France when it comes to food.

But food is no reason to not travel to the UK because it is a very beautiful country and so is France. Therefore I would probably split my vacation and visit south of France, skip north of France and travel to UK instead. Also a good chance to compare food.

I have had good and bad food in both the U.K. and France. Eating out is more expensive in France and don’t even think about turning up at a restaurant at 1.40 or you are likely to be told that the kitchen is closed! It’s true that many French restaurants offer similar menus, but in the U.K., the variety is more related to different ethnicities running restaurants such as Indian and Chinese people.

I spent 7 weeks in France in May/June. Most items at French supermarkets are more expensive than in the U.K. other than wine which was significantly cheaper. Cheese, chicken and salmon were all at least double the U.K. price. Fuel is slightly cheaper in France.

Most U.K. museums have free entry, which can make a big difference to your wallet.

The weather is likely to be better in France (other than Brittany and Normandy).

There are pros and cons for each destination and asking strangers on this forum who don’t know your interests may or may not help in making the decision that is ultimately down to you.