Hi, We have 3 kids under 7 and travel through France a fair bit. We tend to be using hotels purely as a stopover, so not bothered about pools/uniqueness etc, and we've found campanile chain to be good - they usually have several rooms with connecting doors (chambres communicantes), so you can put the kids in one room and not have the problem of what you do in the dark room when they're asleep. (We've always had a twin room and the kids have fit in two beds/a kingsize ok, though guess this'll change as they get bigger.) We did the same in a premiere classe this year too - more budget, but fine just as a stopover. Have a good holiday!
We did a road trip through to Italy last year. A night in Belgium, one in Germany, one in Florence - 4 night stay in Rome. return journey - one night in Milan, one in Alsace, one somewhere in the Champagne area and then home.
It was very last minute so we just booked places the night before on booking.com going by ratings. You can cancel for free and sort by useful things such as amenities (pools) or distance. We went in August and there was absolutely masses of availability - if you can bear to go a mile or so from the motorway. We found it much easier to go hotels in in small villages/towns. The standard was still as high as any chain, it was easier/cheaper to park and it was really enjoyable. The worse hotel was the one I spent ages looking for and booked in England (the Milan one) so I have learnt to be more flexible!
We generally use logis too, the rooms are basic but have everything you need, and the food is excellent. Each hotel restaurant will be shut one night a week though, but it tells you on the website which night that will be.
These are family owned hotels all over France. As a tip the French practically invented the internet with Prestel so if a hotel doesnt have its own website then it's probably best avoided.
If you are looking for this summer then you may well struggle to find family rooms now so you may have to split yourselves over two rooms. However our experience is that hotels are often helpful with cots etc (even if they do look like they were first used for Grandmere's Grandmere).
Another good place to look is at www.viamichelin.com. These will also have been inspected and cover a broad range.