The fulmer is a free ring snaffle, with the ring offset to allow for the full cheeks.
It should be used with keepers to keep the bit upright in the mouth, and to support the it. On some the branches of the full cheek have a different curve top from bottom branch, to allow for placememt of the keepers. Any I've seen have had fat mouthpieces.
Before the availability of the fatter french mouth bits, they were very popular starter bits.
Some riders change their horse, they change their saddle, they change their teacher; they never change themselves.
Remember the horse does all the work, we just sit there and look pretty.
I have one with a french link mouth. Its been extremely handy on a mare I get to hack on the trails once in a while that isn't ridden hardly at all and can be a handful, dives and plunges when excited and steering is somewhat optional. The full cheeks help guide her better and the loose rings keep her from being able to take hold and plunge as much. Our ride is quieter and more enjoyable together in this bit.
Ask yourself: "Can I do anything about this?"
If you can, do it. If you can't... then you can't and leave it at that. Worrying achieves nothing but stress.