OK, this is a Friedel-Crafts reaction. Essentially, I think you have the right idea, but the wrong outcome.
I would assume (and I may be wrong) that the chrloride would be the atom to interact with the catalyst in preference to the fluoride - probably because of the higher availbility of the lone pair, and the relative weakness of the C-Cl bond.
The rearrangement part is correct, though I think you may end up with a mixture of products.