Faro's low-slung terminal, with its whitewashed simplicity and Algarve breeze drifting through the arrivals hall, is a fitting endpoint for a journey that requires real planning, since there is no nonstop business class from New Orleans to Faro. The honest answer for anyone researching this route: you'll connect, most efficiently through Atlanta on Delta, or through London and Lisbon on British Airways and TAP Air Portugal, respectively. My preferred routing after many attempts has been Delta out of MSY into Atlanta, then a transatlantic hop in Delta One, followed by a same-day or overnight link to Faro via Lisbon on TAP. Delta One's suites—fully enclosed on the 767 and A330neo fleets that dominate Atlanta-Europe pairings—offer the sleep quality this itinerary demands, given the total journey often exceeds fourteen hours door to door.
The alternative worth serious consideration is routing via London on British Airways, using their Club Suite product (found on the 787-9 and A350 fleet) for the transatlantic leg, then a short Club Europe hop down to Faro from Heathrow's Terminal 5. This works particularly well in shoulder season—April, May, September, and October—when Algarve-bound leisure traffic hasn't yet peaked and connection times through Heathrow tend to run smoother, with less congestion at security. My insider tip: book the TAP or BA connecting flight into Faro for a midday arrival rather than late evening, since Faro's taxi queue and rental car counters thin out considerably after the morning wave of charter flights from Northern Europe clears out.
TAP Air Portugal, worth flying at least once for the novelty, operates a respectable business class on its A330neo and A321LR aircraft for the Lisbon-Faro or Lisbon-US legs, though their long-haul hard product trails Delta and BA in privacy and finish. Given the routing complexity and fare volatility across three carriers and multiple hub cities, I'd strongly encourage setting up fare alerts specifically for this New Orleans–Faro corridor rather than checking manually, since award and discounted business fares here shift quickly and rarely announce themselves twice.