BTW, I found this OW airfare from DFW to NCE for $581 including tax. It is American Airlines to Boston and then AerLingus to Nice with a connection in Dublin. From Boston it is $433 including tax. It was quoted on Orbitz, but you can book directly with AerLingus.

OW going DFW to Funchal is a little trickier and is $648. American to Chicago, then AerLingus to Dublin, then BA to Funchal with a connection in London Gatwick.