We are a family of 5 which includes three school age children. We've been approached about a home exchange possibility in Montpellier. We would probably tack on a second week in Spain. Happy to explore the coast and beach for a day or two. Day trip to Carcasonne. Just wondering whether there's enough else to do there for a week or whether we should try to find another exchange possibility. Appreciate your thoughts.
Montpellier is a nice, smaller city. It doesn't have 4-star sights, but would be a nice place to hang out for a week, with side trips. In addition to Carcassonne, you can go to Nimes (the kids will LOVE the audio tour of the Roman arena with its explanations of how the gladiator system worked, and the town itself is very nice), and even Arles or Avignon. A quick look shows that Nimes is a half hour from Montpellier, and the other two are around an hour. I'm not sure of the logistics of getting from Montpellier to Pont du Gard, but that would be quite a sight for your kids (and you). I haven't been to the coast near Montpellier, so I can't comment on beaches and the like. I believe positive things were said about Sete on this Helpline - a search should turn these up.
I'd also recommend a day trip to Sete. It's worth just taking a stroll around of the port area.
Montpellier is a great location for day trips. In addition to Nimes and Pont de Gard, I'd suggest stopping by Uzes.
I've spent quite a lot of time in that area and love it. Daytripping from there is easy and there's a lot to do. In addition to places already suggested, there is the Camargue, which is very interesting and would be a fun day trip for your family. You would also be close enough to visit Arles and Avignon as well as other places in Provence. I think you'll find that a week isn't long enough!