Delta, Air France, and Emirates has round-trip flights from Dallas (DFW) to Mumbai (BOM) for $808-$859 with a connection. Flights September, October, March, April, and May. Extended weekends available. Flight may operate as a SkyTeam code-share Delta/Air France.
Turkish has fares for about $769; but those require an overnight connection.
It’s probably worth paying the higher $859 fare for Emirates rather than Delta/Air France
A Carry-on bag and also a personal item is allowed for free. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.