Here's an answer by /u/JimeDorje that might help.

This is and has been possible in Europe.

Portugal has two Languages. Mirandês and Portuguese. France and Italy had several and still do to a lesser extent. The UK has 4(Welsh, Irish, (Scottish) Gaelic, Scots and English) Belgium has two* three official languagesDutch (Flemish), French and German. Spain has 3 Catalan, Basque and Spanish.

European countries are a lot smaller so pushes for a common tongue tended to be more successful.

Anyway here's an answer explaining France by /u/Idjet

Here's a thread on the Basque region of Spain. The answers are older and may not be up to current standards. Here's an answer about Welsh by /u/The_Manchurian.

Edit:* Belgian languages mentioned by /u/woollenarmour

The simple answer is colonialism and the resultant nationalism. Anti-colonial Indian nationalism was the result of British colonial rule and is what resulted in the creation of the Indian nation state. After independence, India adopted a democratic constitution that allowed for internal dissent which is not the situation in Europe. When anti-India, anti-Hindi sentiments were strong in Tamil Nadu, for instance, they were allowed to be expressed with the election of Dravidian parties within the framework of the Indian constitution which had actual power. It’s not the case in Europe, where Euroskeptic parties are allowed to exist in the European Parliament but the EP is not a powerful entity. What has allowed the Indian union to survive is this structure which allows for multiple ethnic and linguistic groups having representation.