Nantes remains one of France's most underrated regional gateways, and the truth is there's no nonstop path to get there from Louisiana—every itinerary in business class from New Orleans to Nantes routes through a major European or East Coast hub, with a connection on the European side almost always required since Nantes Atlantique receives no widebody service. The most reliable combination pairs Delta's transatlantic metal out of MSY (typically via Atlanta or JFK) with a codeshare partner like Air France into Nantes, or alternatively routes through Paris-Charles de Gaulle on Air France directly, then down to Nantes on a short regional hop. Delta's A330 and A350 business class cabins, both featuring fully lie-flat suites with direct aisle access, handle the long Atlantic crossing well, while Air France's Business class on its A220 or A319 regional fleet covers the Paris-Nantes leg competently, if without lie-flat seating given the short duration.
My preference on this routing is to build in at least a two-hour buffer at CDG, ideally clearing through Terminal 2E and using the Air France lounges there before the final short hop—Nantes' domestic-style terminal has minimal amenities, so you want your comfort and coffee handled before wheels-down. Lufthansa is a viable third option for travelers willing to route through Frankfurt or Munich, and their long-haul business class product (increasingly refreshed under the Allegris rollout on select aircraft) is worth chasing if your dates align with newer equipment—though Allegris isn't yet fleet-wide, so it pays to check aircraft type before booking. An insider trick I've used repeatedly: booking the MSY–CDG segment separately in business while ticketing the CDG–NTE hop in economy or premium economy often prices out lower than a single through-fare, since Air France's short-haul business product commands minimal upcharge anyway.
Seasonality matters enormously here—January through March and again in October and November consistently produce the softest fares, as Nantes' Loire Valley tourism surge (late spring through summer) pushes demand and pricing upward. Given how fragmented and fare-class-sensitive this routing is, I'd strongly recommend setting up automated fare alerts rather than manually checking, since availability on these connecting itineraries shifts quickly and rewards travelers who can move fast.