There is no nonstop path linking these two cities, which means business class from Pittsburgh to Bordeaux always routes through a European or East Coast gateway, and the connection you choose matters more than the fare itself. Delta's most sensible routing pairs a PIT-to-JFK or PIT-to-Atlanta domestic segment with a transatlantic leg operated in Delta One, often on the A330-900neo with its suite-style seats and sliding doors, connecting onward to Bordeaux via Paris on an Air France partner flight. Air France itself offers the more elegant single-connection option through Charles de Gaulle, where its A350 and 777 business cabins feature fully flat seats with direct aisle access on the 350, and where transfer times at CDG's Terminal 2E are generally manageable if you allow at least ninety minutes given the walk between satellite gates. Lufthansa routes through Frankfurt or Munich, and travelers booking Lufthansa should specifically seek out the Allegris business seat now rolling out on select long-haul aircraft, since the older business product on some Frankfurt-bound aircraft still lacks the newer suite doors.
Seasonality on this route rewards patience: January through March and again in October and November consistently produce softer demand and better award and revenue fares, since Bordeaux's wine-tourism peak in summer pushes prices upward well before departure. My own preference after many transatlantic connections through CDG is to build in a longer layover than the airlines suggest as minimum—Bordeaux-bound flights from Paris are often on smaller regional aircraft departing from a different terminal, and rushing that connection after an overnight flight undercuts the entire point of flying business class in the first place.
Given the lack of a direct option, fares on this Pittsburgh-to-Bordeaux corridor fluctuate more than point-to-point routes, so setting continuous fare alerts across Delta, Air France, and Lufthansa is the smartest way to catch the shoulder-season pricing dips before they disappear.