What about this?
ORD to YYZ on AA (could I stay in Toronto for a night?)
YYZ to LHR on BA
(Ground transport to Provence)
NCE to MAD on BA
MAD to ORD on IB
Would this work?
Edited to add - I'd *like* to stay in Toronto, for one or even two nights. It's somewhere I've been wanting to go back to visit.