Winger Mike Roberts touched down twice and Andy Craig added another as the home side trailed 23-22 at the break.
With Andy Henderson yellow-carded, the visitors stretched their lead but Glasgow rallied strongly.
Dan Turner, Kevin Tkachuk, Rory Lamont and Graeme Morrison all breached Bourgoin’s defence, while Colin Gregor’s kicking was accurate.
: Lamont, O’Hare, Craig, Henderson, Roberts, Gregor, Beveridge, Tckachuk, Thomson, Murray, Turner, Hayter, Swindall, Petrie, Barclay.
: Parks for O’Hare (75), Morrison for Craig (69), Barrow for Henderson (50), Pinder for Beveridge (60), Harrison for Tckachuk (40), Lawson for Thomson (64), Hamilton for Hayter (77).
Carmona, Janin, Bousses, Giorgadze, A. Forest, Boyet, M. Forest, Milloud, Bonet, Cardinali, Del-Fava, Pape, Frier, Bonnaire, Jooste.
: Campeggia for Boyet (40), Peclier for M. Forest (40), Peyron for Milloud (55), Mazel for Del-Fava (69).
: Tim Hayes (WRFU).