Most of the larger ships of the main cruise lines would probably suit you - check whether they have kids clubs etc. Some will have waterslides, some will have sports courts, some will have rides etc.
Personally I like NCL, as it's very relaxed, drinks packages can be included at very reasonable cost etc. To me, it's the best bang for your buck. They have kids clubs, and lots to do - our kids loved them.
Some of the massive Royal Caribbean ships are really good for kids - and can be good value if you are not much of a drinker as the base price can be goo- drinks and drinks packages can be very expensive on RC, but if you are happy with basic buffet drinks, and the odd glass of wine/cocktail that you buy as you go, then you'll be fine.
Bear in mind, on a European cruise, it's often very port intensive, so you don't spend as much time on the ship as you would if you have lot of sea days. So consider this when choosing a ship - especially if the larger, all whistles and bells ships cost more. I'm sure you'll have a great time, whichever ship you choose.