There's a particular satisfaction in routing through a hub you actually know well, and after years of piecing together journeys from Birmingham, Alabama to France's second city, I can say plainly: there is no nonstop option, so business class from Birmingham to Lyon always means a connection, typically through Atlanta, New York-JFK, or Paris-Charles de Gaulle. Delta and Air France, joint-venture partners, offer the smoothest routing—Delta One out of Atlanta on widebody equipment, transferring to an Air France short-haul business cabin into Lyon-Saint Exupéry. United routes through Newark or Washington Dulles with its Polaris product, connecting onward to Star Alliance partners since United doesn't fly this final leg itself. Total journey time runs around 9.5 hours of actual flying, though with connections you should budget a full travel day.
My strong recommendation, built from repeated trips, is Delta One via Atlanta into Paris, then the Air France transatlantic-to-domestic transfer at CDG's Terminal 2E—arrive with at least two hours if you're checking bags internationally, as French customs and the RER connection zone can bottleneck during summer peaks. Air France's A220 or A319 business class on the Paris-Lyon hop is modest compared to the long-haul cabin, but it's short and efficient, and Lyon's compact airport means you're through immigration and into a taxi within twenty minutes of landing—a genuine advantage over larger French gateways.
Insider tip: book the Atlanta-CDG leg specifically on Delta's A350 with the newer suite configuration rather than an older 767, as seat availability and consistency vary widely by aircraft on this exact pairing—call reservations to confirm equipment before ticketing. January, February, March, October, and November consistently offer the softest business fares as leisure demand to Lyon's wine country and Alps access dips. Given how much these fares fluctuate week to week on connecting itineraries, setting up automated fare alerts for this specific city pair will save you both money and the tedium of manual checking.