I am an Indian citizen staying at India. If I marry a British citizen or French citizen then how will I get EU citizenship ?
Citizenship of the European Union is granted by the member states of the European Union according to their national laws. That is, any citizen of a member state is automatically also a citizen of the EU, and there is no way to be a citizen of the EU other than by having the citizenship of a member state.
The UK generally requires you to reside in the UK for a number of years before you can naturalize. The residence requirement is reduced from 5 years to 3 years if you are married to a citizen of the UK. In France, you can naturalize after four years of marriage to a French citizen if you live in France, or after four or five years, depending on other circumstances, if you live abroad, if I understand the relevant web page correctly.
As the spouse of an EU citizen, you would be able to move with your wife to any other EU country, as well, with relatively few formalities, and then you would normally be able to naturalize in that country after having lived there for a certain length of time. The details vary by country.
Ever heard of BREXIT? I would stay away from French women, too. Look for an Italian, or Danish. Just kidding, of course. There is no such thing as EU citizenship, anyway. You will have to check the citizenship laws of the respective country. Google is your friend. E.g.: https://www.bmeia.gv.at/en/austrian-consulate-general-los-angeles/service-for-citizens/documents-and-authentications/austrian-citizenship/