Airport transit visas are a requirement for some passengers to get a visa even for an airside transit (i.e. luggage checked through, no need to go through immigration/passport control). This is not your situation.
In you case, as both flights are booked separately, you need to enter France/the Schengen Area (i.e. go through immigration/passport control) to reclaim your luggage, go through customs, go the the Air India check-in desk, and drop your bags, before exiting France/the Schengen Area (passport control again).
For this, you need a "full" visa (type C). If your Irish residence permit is as a "family member of an EU citizen", there are special rules, but otherwise an Irish residence permit does not change anything, you need to go through the usual process to get a full visa from the French embassy or consulate serving your area, which could take a little while, especially these days. Being an EU resident, and needing the visa just for transit should help in the process, but you'll probably need quite some documentation.
Don't forget that if you have to do the same trip on the way back, you'll need a visa too, so you should ask for (at least) a dual-entry visa.
And that's just the regular non-COVID rules. There may be additional COVID-related regulations at play, haven't checked what they would be in your specific situation (landside transit by a non-EU national who is an EU resident).