In Paris, the home side led 27-11 at half time and then had two penalties from Diego Dominguez before an injury time try from Christophe Dominici concluded the scoring.
Ulster scored the game's opening try when Tony McWhirter raced onto a chip through from Pddy Wallace to leave the visitors trailing 6-5 at the end of the opening quarter. However, the French opened up and ran in three tries - all converted by Dominguez - to set Ulster a mission impossible task in the second half.
Connacht started off brightly at home and led 14-5 thanks to tries from Dan McFarland and Tim Allnutt. But Sale out-half Charlie Hodgson was in impressive form and two penalties and a conversion of a Richard Wilks try put Sale 18-17 up at the break.
Sale went further ahead with a 48th minute try converted by Hodgson who also tagged on a penalty but replacement Mark McHugh landed two penalties to leave just five points separating the sides. Hooker Andy Titterrell scored his side's fourth try which proved decisive although Connacht did score a late try.
In other games played this afternoon,(Pool 5) Montferrand defeated Northampton Saints 21-15 at Franklins Gardens while Cardiff were much too strong for Glasgow the Welsh side winning 46-7 at the Arms Park, Iestyn Harris scoring three tries.