What do you think will happen if Indian Navy uses missiles to take out your defence positions? There are no missile defence system in this world with 100% success rate. And Indian Navy has good AA missiles too. In tiat case, loss of aircraft/warships will be very minimal.
If the occupying forces try to attach IN using air crafts, they will face loss too. How long do you think that French forces will be able to hold without proper cover from continuously incoming missiles? And, taking into account the size of Indian Navy and French Navy, sending reinforcements to the occupying forces will be more than difficult for France.
And what missiles do you have? Brahmos III is far away from service, your ballistic missiles are not accurate enough to guarantee major damage to the defences unless going nuclear, but even then French troops are NBC protected. The best SAM IN has is SA-N-7 which are no better than our modernised SM-1s. Our ships come with Asters upgraded Standards and Crotale NGs and can operate very far away from air bases on the Subcontinent making coordinated air-strikes lazy at best. Our ships, subs and aircraft carry enough Exocets to swamp the defence and sink most of what will come before it. If anything of what the USN officer said about IN is true, it won't be combat ready if it did come down to it. Between the Horizons, SAMP-T batteries and Rafales guarding the islands, the amount of airpower required to defeat it would be tremendous. We do have datalinked AWACs so our situational awareness will be much better meaning a higher IAF loss rate.
The real question is if your ballistic missiles can take out the airbase, SRBMs are useless against Aster-30 and your land launchers are too far anyway. Are there enough MRMBs to pepper the area to get enough damage to shut it down? They were not made with precision strike in mind so I think not likely. IAF has to shut down the French Navy and Air Force if it is going to retake the island or any force will not be safe making the journey. SSNs will be lurking the waterways and they do have uplinks to extensive European observation SATs, not just Helios 2 constellation but all partner constellations which is on par with US assets. Targeting ships will be easy for us, not so easy for India as they don't even know what is going on off their coast now. Throw in some SCALP attacks to degrade India's tracking assets and we can leave a big black hole.
The biggest problem will be logistics, we can set up enough for a month in the initial convoy, but it would have to be resupplied every month. Lacking A400M would require conversion of Airbus freighters to make an air bridge and we would have to charter the Ro-Ros we have for emergency transport missions. Keeping a CSG on station for more than 6 months won't happen with only one CVN, so we would have to rely on the airbase and maybe make another as a back-up. Under the protection of land based air power the task force would have to keep vigilant patrol over the island(s) and all convoys would have to come far South out of wandering IAF patrols.
Now, if Indian forces can survive a couple hundred Exocets, several hundred Asters and land enough troops to dislodge several thousand Marines, it can take it no question. Otherwise it would have to try and patrol the vast expanse of the IOR trying to hunt for our resupply convoys and Air Bridge and try to starve us out. They would be so far South, India wouldn't be able to look out there for long. In the meantime, France would control all the major choke points of the world's sea lanes: Red Sea, Persian Gulf, The Cape and Straights of Malacca. Targeting Indian shipping from these locations could bring GoI to the negotiation table before repatriation is even attempted.