India does not tax the inheritance
The Indian side is straightforward. India has no inheritance tax and no gift tax, and the income-tax law exempts anything you receive under a will, by inheritance, or as a gift from a relative, under the proviso to Section 56(2)(x). So money or property coming to you from India is tax-free in India on receipt. A large gift from someone who is not a relative can be taxable in India above ₹50,000, but a genuine inheritance or a gift from close family is clear. And because India taxes neither the estate nor you as the beneficiary, there is no Indian tax to set against a French bill.
So the whole tax question is French, and there is one French rule that surprises NRI families more than any other, which is worth understanding before you assume the Indian inheritance is safely offshore.
France taxes the heir on the worldwide inheritance
French inheritance and gift tax is charged on the person receiving, the heir, and the key rule looks at where the heir lives, not where the deceased lived. Under French law, if you as the heir are tax-resident in France and have been resident in France for at least six of the ten years before the transfer, France taxes you on the inheritance of worldwide assets, including everything you inherit from India. That is the sharp surprise: even if the person who died was Indian, lived and died in India, and left only Indian assets, your having been resident in France long enough pulls that Indian inheritance into the French charge. If you have not met the six-of-ten-years test and the deceased was not French, only French-situated assets are taxed.
What you pay depends on your relationship. In the direct line, parent to child, there is an allowance of around €100,000 per child, renewable over time, and then progressive rates rising to 45 per cent on larger amounts. Between siblings the rate is higher, and for a non-relative it reaches a flat 60 per cent, so who leaves you the asset matters a great deal. There is no inheritance treaty between France and India, the income-tax treaty between the two countries does not cover inheritance, so you cannot look to a treaty to divide the tax. And the domestic credit French law gives for foreign death duties is worthless here, because India charges none. Our role is the Indian end, which your French notaire and adviser will need: the legal heir and succession paperwork, a valuation of the Indian asset, a certificate confirming no Indian inheritance tax is due, and repatriation of the inherited funds out of India to you.