How tight is accommodation in July/Aug?

You have to be careful with dates around weekends and especially end of July/beginning of August, or around July 14th, when lots of French people go on vacation. In some areas hotels, at least the cheaper ones, will be full. And if there are 5 of you, it will be more difficult that for one or two.

I went to Rouen/Paris in July a couple of years ago and had no problems find a room. If the first place we looked at was full, the second place tended to have rooms, so it was pretty easy. These were low budget hotel rooms.

I think that in summer French people tend to head south, so if you're doing the north of France you shouldn't have too many problems.

I like to have the flexibility of not having a set-in-stone itinery, but if you're travelling with a slightly larger group, including children (?) it could be worth booking part of it. Or you could always book just a day ahead, ie if you decide you're going to Paris tomorrow phone round or pop into an internet cafe that day and book somewhere to save you and the family wandering the streets when you get there (though I like that bit, the wandering round a new town not knowing where you'll end up staying).

You'd better book "as you go", but more than a day before, more 2 or 3, which leaves you flexibility (I suppose you have a car?) and some safety margin...Even in "less" touristy areas, it can be busy: not only do we receive some 75 millions visitors every year, but France is the favourite destination for our holidays ;-))!

Paris won't be full, but Britanny is a very popular destination (no, not all French head south!)
It certainly is best to book ahead if you're demanding with hotels. If not, you'll find ways. You can also stay at Gites ruraux, that are increasingly popular (and cheap).

Paris offers plenty of hotels throughout the city, so you wil have a flexibility, despite going during the peak tourism season. You might have to suffer a little on the type of room or location of it, but for the most part you will be fine.

Thanks,
TG