Cyprus remains one of the more logistically interesting business class puzzles from the Gulf South, and there's no way around it: business class from New Orleans to Larnaca requires at least one, usually two, connections, since no US carrier or Star Alliance/SkyTeam partner offers anything close to nonstop on this pairing. The most reliable routing I've booked repeatedly funnels through Frankfurt or Munich on Lufthansa, then onward to Larnaca on a regional configuration, while Air France's alternative via Paris CDG offers a similar two-stop rhythm with Cyprus Airways sometimes handling the final Athens–Larnaca or Paris–Larnaca leg under codeshare. Lufthansa's new Allegris business class, where available on the transatlantic MSY-to-Frankfurt equivalent routing (realistically you're connecting through Atlanta or another East Coast gateway first, since MSY itself doesn't have widebody service to Europe), is worth chasing specifically for the door suites now rolling out on select 787 and A350 aircraft.
My strongest recommendation after flying this corridor several times: build in a Frankfurt or Paris layover of four-plus hours rather than the tight 90-minute connections online tools default to. Both FRA and CDG can be unforgiving for jet-lagged business travelers navigating passport control and terminal transfers, and Cyprus Airways' Larnaca-bound flights often depart from satellite gates that require extra walking time. If Air France is your carrier of choice, request early boarding through CDG's Terminal 2E business lounges — the Salon Marco Polo or La Première spaces make the layover feel less like a chore and more like an actual rest stop, which matters enormously on an 11-hour-plus total journey.
Seasonality favors the shoulder months heavily here — April, May, September, and October consistently produce the best business class award and revenue fares, largely because Cyprus's peak beach season (June through August) and the winter holiday crunch push premium cabin demand and pricing upward. Given how thin and variable premium inventory is on this Gulf South-to-Eastern Mediterranean pairing, setting up automated fare alerts is genuinely the smartest move you can make before committing to a routing.