This matter can be discussed or studied in two ways. Either you first select the aircraft and then find the suitable carrier for it ...or.... you first select a carrier and then look for aircrafts that can be operated from it.
This is because carriers not only differ in their size of deck and displacement but also in their method of aircraft launch technique. Bigger super carriers use steam catapults and arrestor wires to launch and recover the aircrafts. US carriers use this method. These are called CATOBAR carriers. CATOBAR stands for Catapult Assisted Takeoff but Arrested Recovery.
On the other hand, most Russian, UK and Indian carriers are small and use ski-jumps to launch aircrafts. Ski-jump enables the Adrimal Groshkov to use Mig-29K. These are STOBAR (Short Takeoff but Arrested Recovery) carriers.
http://www.defenselink.mil/DODCMSShare/NewsPhoto/1998-05/980409-N-8890B-003.jpg
Indian Carrier Vikrant first operated Sea Hawks and to be able to operate Sea Harriers, a ski-jump was added to it.
A carrier fitted with ski-jump and arrestor wires can be suitable for Pakistan too. JF-17 needs to be heavily modified for carrier operations with overall strengthening of structure, a fully redesigned landing gear, modifications required for full-time operations in completely humid environment, a lower stall speed, ability to fly at required AoA and a good bring back capability etc.
As far as I understand, bring back is about landing at slow speed while carrying a good payload. For landing, the carrier aircrafts have to slow down and slowing down with a heavy weapon load is often not possible. An aircraft that can generate huge amounts of lift even at slow speed is better suited for carrier operations.
Another important feature of carrier aircrafts is their lower stall speed as compared to land-based aircrafts because deck runway is small and a high speed landing is not possible. High speed landing will require a long runway. This is perhaps the reason that Mirage series aircrafts were not used onboard the aircraft carriers.
French Navy had to use US F-8 Crusader as shipboard air superiority fighter. They had Etendard and then Super Etendard as shipboard attack aircraft.
Right now the trend is to have a truely multi-role aircraft on the carriers exemplified by Rafale, Hornet/Super Hornet and Su-33 or Mig-29K.