There are literally hundred of board manufacturers out there. This is where I normally say to work with a good local shop. But a lot of people are buying gear online, so I also usually recommend some online sites that have a reputation for making good recommendations (e.g. The House rusty gets credit for this link). The key is to call and talk to people because the online information to tell what you are buying is lacking pretty much everywhere you go. However, it seems kind of silly for someone in France to buy a board from the US. I don't have any links for online snowboard shops in Europe, but if you hit my website's shopping link page, Google might pop up some European links on the Google ads.
Fogdog has a good buyer's guide that covers the basics.
But,as has been said a million times before. get boots first and make sure they are comfortable. There's an old saying, you date your ride, but you marry your boots. Finding a local shop where you can try out boots is a must. As long as you're going to get set up and use a shop to get boots, you might as well use the relationship to do a package deal. For the wife, beadvised that women generally have small heels so pay special attention to the fit there and consider custom fitting too. For a beginner snowboard, the most important thing at your level is to get the flex right. If you go too stiff, you will be on the road to be a terminal intermediate. If you go to soft, speed will not be your friend and that will slow your progress too. Length is a critical factor too, but that is easy to get right. At this level quality of manufacture is not super critical because you're probably not going to be stressing the equipment and you won't be finding the top quality in this level gear anyway. Just about any manufacturer is going to have a choice that will work for you, but if I had to recommend one it would be Nidecker. You're probably not going to be able to tell much difference in how the quality of a binding impacts performance, so pick one that is a sturdy design (most people can spot cheap material a mile away) and that you feel comfortable with getting into and out of.(pick your boots, then demo the bindings in a shop with your boots on).