I was expecting some discussion about technical points to prove me wrong.
Actually, it is not a question of look (I personally think they 'look' the same, but it I reckon it is subjective), it is a question of components implantation.
They follow exactly the same pattern and exact 'locating' for each axis, wheels, levers, gears etc.
That is where I say it can not be a coincidence.
In the past, I have worked on 'assignments', where 30 or so designers had to create their own solution to a given mechanical challenge (design of a pump for example), and sometimes even using a set of imposed components (which is not the case in our movement, as JLC is not 'buying' components from outside suppliers, so they have total freedom of design for each of them).
And, even with some 'standard' elements to integrate in the solution, I can guarantee you that none of the 30 designed solutions shared any sort of 'similarity' like the 2 movements in question (same dimensions of parts, same locations).
Changing the 'shape' of a plate or a lever doesn't mean the functional design is not exactly the same.
A better example of 'same movement functional design', different 'look':
2 versions of the IWC calibre 98.
All the 'functional design' is the same, only the plates shapes are different
So you see, judging from the 'look' is not enough to tell 2 movements appart. Obviously, in our case (JLC vs FP), the differences are really minor compared to this extreme example above.
I hope you get my point.