I'm spending this season in Chamonix and will be coming back next season as well. The mountains make any ski resort in North America look small and weak. There are absolutely no rules, you can go where ever you want, including closed runs. Google the Mallory off the Aiguille du Midi for easily the gnarlist lift accessed line in the world. You can blatantly endanger the lives of thousands of people by skiing a huge avalanche prone bowl right above the rest of the area and there is nothing they can or will do to stop you. Its absolutely the best ski area i've ever been to (It's actually 7 small areas connected by busses but whatever) and I've done the best powder skiing in my life here, and I lived at Alta/Snowbird for 5 years. As far as parks go, well Les Grands Montets has one, it's nothing special. You can build booters of any size anywhere in the areas however as their are absolutely no rules.
Make sure you have avalanche gear (beacon, shovel, probe etc) because anytime you leave a groomed trail you might as well be in the backcountry here.
Your also going to want to have a harness, and bellay device for the Aiguille du Midi. Crampons are nice, but not necessary, I've yet to use them getting off the Aiguille, regardless of what the british tourists will tell you. The same goes for an ice ax, ice screws and a good 30 meter glacier rope. You can get by without all of these but you may well pay for it.
none of this shit is required, they aren't dicks like Baker, Sunshine, Bridger etc. all the North American resorts that insist on holding your hand, but you will want it anyway as you are on your own here.
Where are you going to be living? Are you planning on working in town?