I see that German, English and French mostly share the same basic set of alphabet and these are languages are spoken by whole countries but if you go to India, there is a state with a new alphabet set for their letters.

This suggests to me that states of India weren't able to communicate much when compared their European counterparts. Is my analysis correct, if so, what is the reason for this to happen?

See, Kerala, Tamil Nadu, Karnataka, Maharashtra etc. All of them have different alphabet even though they are directly neighboring places