Would I be able to connect this to a French drain? Or will the depth of the French drain be to deep for the catch basin?

A french drain can be connected to the catch basin. It is recommended that non-perforated pipe be used until the pipe is more than 10' away from any structure. Beyond this point you can use perforated pipe. French drains are made with perforated pipe. Having the 10' buffer will prevent water from draining into the ground immediately adjacent to the building which could lead to settling, water in the crawl space or basement, or other structural damage.