They are not necessarily called French Links. A french link snaffle is a bit broken twice with a flat piece in the middle. There are many other bits that fit the qualification of a "thick snaffle broken once or more.."
Dr Bristol (generally the piece is bigger in the middle and lays at an angle, still very gentle though)
A regular broken once snaffle, fits that qualification
You can also have a broken snaffle with rollers.
There is a snaffle that is just the french links linked across (IDK if there are 5 or 6 of them, I forget what its called)..
A happy mouth mullen mouth or rubber mullen mouth is also really gentle, even though its not broken.
Anyway I didn't necessarily mean french link only, or I would have said french link. There are several bitting options, and really depends on what the horse likes best. French links are a good option because they lay relatively flat in the horse's mouth, but they aren't the only bits that do so. (any bit that is broken two+ times will.. and some may have rollers [which a young horse may respond to])
I would pick one gentle bit and stick with it for a while. Once he has the basics down, you can confuse him by switching bits. =]