How to find quiet place to stop close to a motorway junction?

As you're in the UK, the book Off the Motorway, while dated, is still useful. An adult passenger can scan ahead. Since it was published, pubs have become more family-friendly if you want a sit-down meal, and searching "family pub" in Google maps, scrolling to the area around the next junction works well. Or just drive to a pub and ask.

I also tend to have a young child with me when driving long journeys, but come up with a planned stop (often somewhere that looks suitable for a picnic), using the services if a toilet stop is called for earlier. A theme helps here; I've routed by looking at a map of castles before, and picking ones where you can park/picnic for free.

In France, if you route along the D-roads for a bit (speed limit generally 80km/h so you may not want to use them for the whole day) you'll often pass through towns and villages with nice places to stop. However the Aires on the motorways can have more available toilets than having to visit a bar in a village, and many small shops shut for lunch. Look for the aires with fewer facilities, and take your own food, if you want a quieter experience. An alternative (at least in normal times) is a big out-of-town supermarket, which will often have a cafe. I tend to do this as long driving days are often moving from one campsite to another and I'll want some shopping. There's generally no problem just parking as using the facilities.

My experience with motorway services is that in most places, outside of the extreme crowded times, they are mostly clean enough and acceptable.
On those days there are traffic jams on all motorways also the smaller towns and parks near motorways will struggle with the pressure.

In France, the motorway services on the toll roads are good, do not leave the tollroad as that might require paying extra.

When on a non toll road, look at a map or on your satnav for a small town or village with a park. (In these COVID 19 days some parks have limited access.) Most of these villages will have a cafe of some sort which has toilets or there will be public toilets near. On busy days these do get used much and will be no more clean than motorway services toilets. And for the same reasons.

Unlike the UK, the service area in the other countries on your lists are right on the motorway and there are also rest stops which often have parking, toilets and play areas.

Do not wait till your kids 'need the loo' but plan ahead and stop when you predict they will need them soon.
Kids can sleep while driving so stops for naps are not to be expected.

While I do not drive, I have travelled by car quite a few times in all countries you listed, mostly on long distance journeys, motorways as well as smaller roads.