Indian launchers basically use three types of motors- solid, liquid and cryogenic. The solid stages were developed indigenously by India and were used for the launch of the SLVs and ASLVs (both retired now). Incidentally, Indias Agni-I missile was developed out of the solid stage booster used in the SLV/ASLV program. APJ Abdul Kalam was the project director for both the SLV and the AGNI.
The liquid stage used in the Indian PSLV and GSLV launchers is called the Vikas engine. Vikas engine was built with French assistance but it is in no way a modified French engine. It has similarities to the French Viking engine but is vastly different from it, making it unique. But yes French assistance for the development can not be denied. Liquid fueled engines are insignificant for missile programs as they are cumbersome and not preferred by countries operating ballistic missiles. This was the premise on which the French agreed (and allowed by the big daddy) to cooperate with us in the development of the Vikas engine.
The third type and the most complicated to design and develop is the Cryogenic stage. If I am not mistaken, India bought five cryos from the Russians. The Russians did not transfer an iota of technology for their cryos. Here is why-
Even to this day the Americans monitor the use of those purchased cryos to ensure that we dont reverse engineer it. ISRO is not allowed to dismantle even a nut or bolt from those cryos. We are accountable for all five cryos to the Americans. 4 have been used up already and the US is keeping an eye on the last one. If we don use it, it will have to be returned to the Russians. Well that was in the early nineties. Today ISRO has mastered the tech to build a cryo by itself. Our first indigenously built cryo will see action this year when a GSLV is launched. But, think about it, it took us a decade and a half to develop a tech that we could have easily gotten from the Russians loooong back. ISRO has been living under heavy sanctions right from the day we popped a nuke in 1974. The US has effectively ensured till this day that ISRO doesnt get any duel use tech from any country in the world. When such is the case, do you still think our launchers are based on some XYZ countrys tech?