Originally Posted by iridehorses
A Tom Thumb is a specific bit, not just a joined mouth bit with shanks.
A bit without poll action is a simple snaffle and without shanks.
Actually, both you and the OP are correct.
In the US, a "tom thumb" bit is the one with shanks. In many places outside the US (notably Australia), the bit shown in the OP is a considered a "tom thumb." It gets its name from the flattened cheek pieces which look like they have been pressed with a thumb.
The "western" tom thumb vs the "english" tom thumb difference has caused much confusion in internet forums because most people are not aware of the "other" version.
Both are referred to as a tom thumb, depending on where you are in the world.
And to the original question... I have never seen an "english" TT with a french link. Then again, I have never seen all the available bits. :) Is there a reason you need that specific cheek piece?