Glasgow put in a huge effort but still lost out 22-18 to a pragmatic Biarritz side for whom scrum-half Dimitri Yachvili and centre Damien Traille were outstanding.
Despite Dan Parks putting the ball out on the full as he started the game, it was Glasgow who took the early initiative at Firhill.
The French side were unsettled by Glasgow's early tempo, giving away a penalty six metres within their half in the fourth minute which Parks steered home.
In the seventh minute centre Rob Dewey drove forward off a pass from Parks and when the penalty was awarded at the subsequent ruck, Parks made it 6-0.
Biarritz were unsettled and it was no surprise when their scrum gave away another penalty, kicked by Parks.
The French side then settled, with Yachvili and Traille contributing a penalty and drop goal respectively in quick succession.
However, when a penalty was reversed in Glasgow's favour Parks eased his side 12-6 ahead with a long-range penalty.
Glasgow continued to have the better of possession as the half drew to an end but a penalty from Yachvili and drop goal from full-back Marcello Bosch ensured it was 12-12 at the interval.
Parks began the second half with his fifth penalty but Biarritz raised their game, putting the Glasgow line-out under pressure.
Glasgow were trapped in their own 22 and when loose line-out ball from Tim Barker ended over the home line, Magnus Lund was first to it for the opening try. Yachvili converted to give the visitors a 19-15 lead after 50 minutes.
Glasgow got back on the front foot thanks to a break from Thom Evans and a drop goal from Parks on 59 minutes made it 19-18.
However, the gap was widened again on 66 minutes when Yachvili struck a magnificent penalty from the left-hand touchline.
Glasgow then huffed and puffed without ever putting the visitors' defence under real pressure until deep into stoppage time.
And Glasgow were lucky not to concede a second try when left winger Julien Peyrelongue just failed to reach a kick threaded through by replacement Laurent Tranier.
Before Will Greenwood started breaking down moves off the field, he was doing the business on it - and no match better illustrated the type of marauding centre he was than in a virtuoso performance against Wales.