Strasbourg's absence of direct long-haul service means the real strategy for booking business class from Minneapolis to Strasbourg lies entirely in the connection you choose, since no carrier flies this pairing nonstop. The most reliable routing pairs Delta's transatlantic metal — often the A330neo or A350 in Delta One suites — through Amsterdam or Paris, with a short regional hop into Strasbourg's compact SXB airport, which has no lounge to speak of, so you'll want to have cleared any relaxation needs before that final leg. Air France offers the more elegant option for francophile travelers, routing through Paris-Charles de Gaulle in their newer Business class cabin (with the reverse-herringbone seats now standard on refreshed 777s and A350s), landing you close enough to Strasbourg that a connecting flight or even a scenic TGV transfer from CDG becomes viable — and in my experience, the train can actually beat waiting on a tight regional connection during winter schedule disruptions.
Lufthansa, routing through Frankfurt or Munich, is worth serious consideration for travelers chasing seat innovation: Lufthansa has begun rolling out its Allegris business class on select long-haul aircraft, though availability on MSP-originating itineraries can be inconsistent depending on aircraft swaps, so it pays to check the specific equipment before booking. My insider tip, learned after several misconnections: build in at least a 90-minute buffer in Frankfurt or CDG for the SXB leg, since Strasbourg's limited frequency means a missed connection can mean an overnight wait rather than a quick rebooking.
January through March and again in October and November consistently produce the softest business class fares on this corridor, as Alsace's tourist season quiets and corporate travel dips between conference cycles. Given how thin capacity is between these three carriers, setting up fare alerts is genuinely the smartest move you can make before locking in dates.