A pair of Ben Blair tries had put the hosts in a commanding 17-5 lead at the break, but three second-half tries put the French back on level terms as the home side seemed frozen by the night's bitter weather.
There was some warming news for Wales coach Gareth Jenkins, set to announce his squad for the Six Nations on Monday, as 2005 Grand Slam winners Martyn Williams and Robert Sidoli made their first appearances of 2007.
A three-week ban for head-butting has kept Williams on the side-line, while Sidoli has been out since November after a shoulder operation. Both played well in an otherwise disappointing Cardiff win.
This has been another disappointing European campaign for the Blues. An opening day win at Bourgoin was cancelled out by four defeats home and away to Munster and Leicester, their 34-0 defeat to the Tigers at Welford Road summed up what has largely been a miserable venture for Blues fans.
The Blues spent the opening exchanges in the Bougoin half and fullback Ben Blair claimed the first try when he hit the line at pace and breezed through a hole in the defence to touch down.
The ex-All Black handed the kicking duties to Nicky Robinson who slotted the conversion and landed a penalty shortly after to hand the Blues an early 10-0 lead. Outside centre Jamie Robinson then put Blair over for his second try before the younger Robinson brother landed the conversion.
It took until just before half-time for Bourgoin to get on the score-sheet when Georgian prop Davit Khinchagishvili barged his way over to make it 17-5 at the break.
It was business as usual after the break when inside-centre Nick Macleod darted through the defence for a try under the posts to give Robinson an easy conversion.
Bourgoin demonstrated the route-one approach for their second try when a 12-man maul bundled flanker Mark Rennie over for a try, while left wing Jean-Francois Coux grabbed a late third try that put Bourgoin back in the hunt.
Sebastian Laloo's conversion of replacement Pascal Peyron's late try tied the scores before Robinson's boot won the game in the 82nd minute.
Cardiff Blues: Tries: Blair (2), Macleod. Cons: N Robinson (3). Pens: N Robinson (2)
Bourgoin: Tries: Khinchagishvili, Rennie, Coux, Peyron. Cons: Laloo (2)