America has been nudging India since long to join an alliance with it, and now its France , an ally of America, calling for the same. India is a non aligned country with an independent foreign policy. It does not allow outside influence in deciding what position it should take on international or national issues.
Does India really need to join such alliances, when it has independently been able to stand its ground, as well as stand up to rogue neighbors like Pakistan and China. India did not beg for help to anyone when in 2017 at Doklam, China threatened it would teach India a lesson like in 1962.
Furthermore, Russia has been a friend of India for 70 years , through the worst of days, yet have never asked India to sign a binding alliance. What for would India agree to sign such a deal with the US that would literally turn India into a lower district of another nation in terms of decision making power.
India shares a very positive relations with France. But France is a part of NATO, a military alliance that has USA as its leader. India is against the idea of forming alliances as it erodes the independence of nations and the world gets divided into hostile power blocks. For this reason India was among the founders members of NAM (Non Aligned Movement).
Referring to a relevant article, as posted above.