If your JFK-CDG flight is operated by AF, it's only available with miles at the low level. I suspect that the flight has low award seats in coach but not in business class. If you can reroute with a DL flight, business class should almost always be available, but probably at a cost of more miles.

You're basically paying for two separate award tickets in each direction, namely USA-EU and EU-Asia outbound plus two more one ways if you return the same way to make a RT. It might be cheaper (in miles) to do this as two separate RTs or alternatively to at least return from Asia using a TPAC routing.

You might also want to check the cost of purchasing a RTW ticket for this, although note that specific booking class availability is required.

BTW, if Asia = India etc. then many of the above comments in this thred are inapplicable as DL normally routes USA to India via Europe.

Also, BTW if less than 24 hours in Europe is enough, this doesn't count as a stopover and is normally cheaper, although I still suspect that it means two separate award tickets.