A lot of things would have changed. And a lot of things would nevertheless have happened.
Let me tell you what all things I think would have changed at the time.
- The peasants and artisans of Mysore would have led a comfortable life for a longer period ( Tippu’s administration was so effective that the British commander who defeated him is said to have observed that the peasant in Mysore was in an even better condition than the best administered regions of the Raj)
- None of the Indian rulers of the time except Tipu had any innovative spirit or curiosity. Tipu was the only ruler of the time who actively pursued the technological developments of the world. You know about the Mysore Rockets, I suppose. Had Tippu won, Indian rulers would have woken up to the need for technological upgrade from the old Mughal artillery. A tie up with France would have meant Indians getting access to that technology faster (War Technology was fast evolving in Europe of the time)
- A modernisation wave would have swept across the militaries of the subcontinent. Tipu’s military was in fact the most disciplined at the time. Not a single soldier of his abandoned him till his last breath. In fact his entire troops died battling with their king. An astonishing achievement for a Muslim ruler fighting with a predominantly Hindu army.
- Indian rulers, who were so oblivious to world developments at the time would have opened their eyes and understood that the world did not revolve around their petty feudal concerns anymore.
- They would have realized that the future ruler of India would be the one who is able to make better alliances and not just on a regional scale but global scale.
- British would have far more zealously pursued their policy of sowing dissent within the Indian rulers and reaping the benefits.
- Tippu Sultan would have not just been remembered as the Mysore Tiger but the Tiger who mauled the leonine Raj. Indian History books would have sung his praise.
- India would be remembering France today like we remember Japan for the help rendered to Subhash Chandra Bose. Indians are usually very loyal and grateful that we even overlook how brutal many Japanese were during WWII. We would have overlooked the brutality that France unleashed upon the Algiers population and would have probably remembered France as a friendly nation for a long time to come (we are friendly nations, btw. I am talking of an emotional connect, I hope you get it)
What things would not have changed?
- British would have conquered Mysore nevertheless. Britain at the time was the America of 21st century. Imagine the US were to decide that it wanted to attack India ( a much larger territory than Mysore) today. It would definitely have a tough time, without doubt. It would not probably succeed in one battle/war. But nevertheless ultimately it would win (lets not get into we have/they have nuclear weapons debate. This is just an example which might never happen). This is because they have a large amount of resources and allies at their disposal than does India. Same way, British Raj at the time had a huge amount of resources (sourced from territories and peoples of the Indian subcontinent and outside) at its disposal. Mysore’s resources in comparison would have been puny. In fact once, Bengal was conquered after the Battle of Plassey and Buxar, the fate of India was sealed.
- Modern day crusade against Tipu Sultan would nevertheless have continued. Many people would have continued to call him a bigot and an iconoclast. I do not want to get into the communal aspect of it, but since you asked I wan’t to stress this point.
Now, I know you asked me what India would be like which means what would it be like today. It’d pretty much be the same since we would still have had colonialism and an anti colonialist movemet and all the associated development for the reasons I have mentioned above.
Hope this helps.