I have been reading about format preserving encryption and would like to use it.
There are many good reasons for using FPE, but this is certainly not one of them.
It's OK to get excited about a solution but you should not apply that solution regardless if it fits the problem.
This reminds me of a developer I knew that wanted to use each and every pattern he encountered. Pattern driven development: "we have this programming pattern, now which problem do we need fixing?"
I would like to know if its a good idea to use FPE after compression or would that even make sense.
No, it doesn't make sense. Compression generally compressed to bytes, and bytes can be encrypted fine. FPE is mainly used where there is no easy byte or bit conversion possible, e.g. when the output needs to be a number or a specific range or characters. The most common example is the format of credit card numbers.
Besides that, FPE may add quite a bit of overhead; you certainly don't want to process 100s of GB of data with it.