Honestly...I wouldn't obsess over bits if I were you. While they do matter, I feel the best thing you can do is use as little "artillery" in the mouth as possible, and use your seat and leg most. When something is working good for you, don't try to fix what isn't broken, after all! ;)
That being said, not all snaffles are created equal. Even when you are using the seat and leg primarily, a horse may just not like the way a bit feels in his mouth. Some horses like a lot of movement, others don't like any mobility.
What is good about a french link is it eliminates the "nutcracker" action you get with single jointed bits. Some horses would prefer that to 3 links though. It all depends.
My pony goes in a french link eggbutt and he loves it. It's a gentle bit and I still barely have to use my hands at all. He goes very light.
I think they are very good bits, very mild. Just give it a try and see if your horse likes it! Here's a full cheek french link. French Link Full Cheek Snaffle Bit - Dover Saddlery.