You really can't get through Eu4 without vassals, this is why some of the most popular idea groups give you the ability to have more vassals. Don't be afraid to go over the diplo limit, if your monarch has good diplo or you have +3 advisers, you shouldn't feel the lost 1-2 points per month.
Vassals go hostile if they think they can get independent. If a vassal is temporarily hostile, its because it sees itself as stronger than you, and is seeking foreign help in its independence war. You are France however, and this attitude will usually vanish if you are that strong. The other factor is the historical rival modifier which burgundy has with France in 1444. This usually means that France has a better time full annexing burgundy rather than vassalizing. For pu's the same holds true, only that the AI seeks independence much more frequently. PU junior partners also have some nasty events such as nobles decapitated which lowers their opinion of their overlord.
Finally, I would say France is not the best nation for a first timer. You start at war, and at least in the early game, you are surrounded by enemies. Of course you will dominate them, but its not the best beginner start. I would suggest Portugal, England, or Denmark, Denmark being the hardest, as your next big game. These nations have the ability to totally ignore Europe after the early game, so one has the ability to build up a huge trade empire before returning to Europe in style.