We've done five trips to Europe as a family of four, including 2 cruise/land combos, and one European chain that we keep coming back to is the Novotel chain. They are part of the Accor brand which includes Mercure, Ibis, Sofitel and a few others, but Novotel is our favourite for families. They have family rooms for four for the same price, or not much more, than double rooms, which can be hard to find in Europe. These rooms are usually a queen sized bed with a sofabed, but usually the sofa has a neat design that folds out as two singles instead of one big bed. This seems to give better support and even though the two beds are only a few inches apart it still helps my kids sleep better to each have their "own" bed.
Another thing we love about the chain is that many of the hotels have absolutely fantastic breakfast buffets. And there's usually a play area in the lobby where the kids can hang out while you check in. We've already booked Novotel hotels in Amsterdam, Ghent, Paris and Dijon for our European trip this summer, and paid less than $150 US per night with breakfast.