I should think your cob probably doesn't like your French link very much because most cobs have low palates and fat tongues, and the link will almost certainly push down on his tongue.
My friends cob uses a kimblewick which is ported and I have a Rockin S raised snaffle which has a broken port and is sweet iron. Both bits are for fat tongued, low palate horses.
Good luck, bitting is a minefield!!
Some people say kimblewick's may not work as it is not a jointed bit, so if the horse is a leaner then they could just grab the bit and pull down