You look at the TP website, and it's got the MAN route with connections to USA, Africa and Brazil. Not South America. If you want South America covered, you'd be looking for a joint IB/BA service to MAD using 50 to 70 seat aircraft. Besides, I can't see that they'd be willing to let MAN be a pretty big spoke for Star Alliance carriers with limited oneworld coverage.
There's no reason to suspect that FR and U2 can't co-exist on MAN-MAD as they'd be after slightly differing markets.