Yesterday.... The problem was that India could never rely on the US for weapons, and meanwhile it did supply Pakistan from time to time, as part of the cold war against communism. Following the 1965 war, the US stopped supplying either country weapons for some time as those weapons were meant to be there against communism not to fight eachother. Pakistan went shopping in China, India which did not/has not got a good relationship with China, developed a stronger relationship with the USSR. Meanwhile India's aviation industry started to develop, and HAL could assemble/produce MiGs. There's also the nuclear issue, and following embargos. I don't know exactly if it covered all the years, but you can understand that it wouldn't be wise for the IAF to rely on aircraft, which are subject to logistical support from a country that will embargo you when you either further develop your nuclear arsenal, or get into war with your #1 enemy. So the industry and air force has been almost entirely been Russian focused, with some exceptions, French as you said, but also British, but not very capable aircraft.
Today.... it's a bit different. The embargoes have all gone, and India can indeed get US aircraft and UK aircraft again. The Su-30MKI deal was already done, same for the Il-78 tankers. For the M-MRCA competition this is fine, F-16/F-18 competing. For the Navy fighter deal, it wasn't an option as the MiG-29Ks were part of the deal for the carrier. The Il-38 are upgrades, they already had those, but P-3/P-8 is being looked at. For the fifth generation, it is not possible to put their money on a US type, because limited tech transfer and no production would put HAL out of a job, or at least not be to the level of ambition they have.
If a Russian type gets picked for MMRCA, it's either to do with tech transfer/logistics, or excessive cost for the Western options. But I would not say it's strictly a money issue. The LCA would have been cancelled by now then, and the carrier deal as well,... it's more about industrial development and prestige!