"My question and frustration was the difficulty of finding a single large room designed for a family of 5 (which to me should not be considered abnormnal)"

I'm probably a bit late on this but it's not the size of your family that is considered abnormal. It's your wanting to put all 5 in one room that's a bit odd.

Doable in American hotels but European hotels are notoriously tiny in the "affordable" price range.

yep - I get the point about connecting and adjoining, especially with kids this age. Our first trip was made when our elder child was 13/14, so we were ok if she was a bit down the corridor, or the kids were both together on a different floor. but with 10 & 12 year olds, assuming they are the ones sharing the other room, I'd want them easily accessible, I think.

You could consider renting an entire dorm room at a hostel. If you look carefully, you could get a perfectly decent, if spartan, place. Say the bed price is 20-25 Euros per night, and you have to pay for 6 beds per night (if it's a 6-bed room, you would probably have to pay for 6 beds, rather than 5). I know this hostel is recommended by some, but I don't know it personally, and the location is a little out of center:
http://www.villagehostel.fr/tar2.htm

There's the official hostels also:
www.fuaj.org

Of course you'd have to specifically arrange with the hostel to have one room blocked just for your family.

What a great idea for budget family travelers, Willtravel! It may not suit everyone, but it is a really creative solution to a problem that often presents on Fodor's.