Bourgoin (9) 21
Rudolf Coetzee of Bourgoin attempts to halt Ulster's Paddy Wallace
Tries: Tchougong, Coux
Pens: Boyet (4) name
Ulster (17) 17
Tries: Dawson, Danielli
Cons: Wallace (2)
Ulster failed to secure their first Heineken Cup win on French soil despite leading for most of Friday night's Pool Two match away to Bourgoin.
Three days after the departure of coach Mark McCall, Ulster made a strong start and tries by Kieron Dawson and Simon Danielli had them 17-9 up at half-time.
But they could not maintain their form, and poor tackling let Arnaud Tchougong and Jean-Francois Coux in for tries.
Ulster clung on for a losers' bonus point but are still bottom of the pool.
The Irish province, under the guidance of acting coach Steve Williams, had a great opening 30 minutes with those converted tries.
But the French hosts, who began the season well domestically, found their feet and gradually inched their way back into an intense clash at the Stade Pierre Rajon.
Having lost heavily to Gloucester at Ravenhill, Ulster's Heineken Cup hopes look over after two games.
They went into the lead against Bourgoin on 12 minutes with winger Tommy Bowe making a good run before feeding inside to Paddy Wallace.
With just full-back Florian Denos to beat, the fly-half drew in his man before passing for Dawson to score.
Danielli pierced the home defence for the second try in the 23rd minute.
The Scot took Wallace's pass and skirted the attempted challenge of Boyet to go over in the left corner.
The conversion from Wallace made it 14-3.
Bourgoin hit back with their first try on 57 minutes as captain Julien Frier powered through flimsy tackles by Wallace and Mark Bartholomeusz, before offloading to Tchougong, who trundled over from 10 yards.
Six minutes later winger Coux to went in on the left wing for the try which put Bourgoin into the lead for the first time.
Bourgoin: F Denos, D Janin, R Coetzee, Y David, JF Coux, B Boyet, M Parra, A Tchougong, B Cabello, O Sourgens, D Fevre, B Williams, J Frier (capt), A Petrilli, M Rennie.
Replacements: JP Genevois, P Cardinalli, C Wyatt, Y Labrit, M Forest, S Laloo, M Nicolas.
Ulster: M Bartholomeusz; T Bowe, A Trimble, P Steinmetz, S Danielli; P Wallace, I Boss; J Fitzpatrick, R Best (c), B Young; M McCullough, C del Fava; N Best, K Dawson, R Wilson.
Replacements: N Brady, D Fitzpatrick, R Caldwell, D Pollock, K Campbell, N O'Connor, R Dewey.