By French standards, there is nothing particularly grand about the Stade Municipal du Hameau in Pau.

It sits in a flat and featureless industrial area in the northern suburbs of the Pyrenees-Atlantiques town, just off the main A64 road that links Toulouse to Bayonne. Its main stand is a grey, concrete affair, thrown up when the ground was renovated almost 30 years ago.

Yet when they ran out onto its pitch on October 12, 1996, a group of players from the Borders thought they had hit the big time. Only a few weeks earlier, many of them had packed in their jobs and taken up the SRU's offers to become full-time professional players. A new era was dawning in rugby and the Borderers, many of them already full internationals, were marking Scotland's first involvement in a European club competition.

Eighty brutal minutes later many of them must have wished they had stuck with their old careers. It was not so much a wake-up call they suffered as a savage assault, ripped from their beds and slammed against a wall. Traditionally the strongest of Scotland's four home districts, they had gone to France confident that they could impose themselves on Pau, hardly the most daunting opponents that country could offer. But they were humiliated 85-28, coughing up 12 tries along the way.

That same weekend, Edinburgh conceded more than 50 points against Bath and Caledonia shipped more than 40 against Ulster. The teams had been conceived in haste - mostly to see off the threat of English club's cherry-picking Scotland's best players - and their performances reflected those makeshift beginnings. Only Glasgow managed to win on their European debut, but that was over Newbridge, effectively a village team, in the lower-tier Challenge Cup competition.

By the end of that season, Scotland's three Heineken Cup sides had played a total of 12 games and returned just one win (when the Borders beat Llanelli). Nor did the Irish fare much better. To all intents and purposes, we were witnessing the emergence of a two-speed Europe, with the Celtic nations consigned to the slow lane.

And yet, within a few years those Irish sides would be the European pace-setters. Ulster won the Cup in 1999 and Munster were the losing finalists in two of the next three seasons. Munster finally put their name on the trophy in 2006, starting a triumphant seven-year run in which they and Leinster won the cup a total of five times.

Remarkable. And all the more so when the record of Scotland's representatives is set alongside Ireland's. The Irish have made an indelible imprint on Europe; the Scots' has been almost imperceptible. The high-water mark - more of a freak tide, really - was when Edinburgh reached the Heineken Cup's semi-final stage in 2011-12. Apart from that, the capital side's quarter-final appearance in season 2003-04 was the only other occasion in 19 years of European rugby when Scotland has had a representative in the last eight of the senior competition.

Against that backdrop, the performances of both Edinburgh and Glasgow this season have been heartening, although not so much so that they can be hailed without qualification. Arguably, the best result of all was Edinburgh's 15-13 away win over Bordeaux-Begles on the Challenge Cup's opening weekend, not least because it was achieved in spite of a horrendous injury list and travel arrangements that would have made Hannibal blanch. Round one also saw Glasgow at their very best, rampant and unstoppable at Scotstoun as they demolished Bath 37-10.

There were wins, too, the following weekend, as Edinburgh used home advantage to squeeze past Lyon, 25-17, at Murrayfield, and Glasgow played crafty, contained rugby to frustrate and, ultimately, beat Montpellier 15-13 in the French side's Altrad Stadium. But Glasgow would go off the boil in the third round, when their indiscipline gift-wrapped points and a 19-11 win for Toulouse, and again in the fourth, the return match at Scotstoun, when the Warriors failed to take their chances and Toulouse completed the double with a 12-9 victory.

The reckoning now is that Glasgow will need nine points from their two remaining games, at home to Montpellier tomorrow and away to Bath next weekend, to go through to the knockout stages. And common sense suggests that the bonus point demanded by that scenario will be more easily obtained on home soil against a Montpellier side whose four straight defeats have already dynamited their chances to progress.

Montpellier lost those four games with Fabien Galthie at the helm. Since when, Jake White, who guided South Africa to a World Cup win in Paris in 2007, has been installed as head coach. White, who got off to a superb start as his new side beat reigning European champions Toulon 16-12 in his first game in charge, is renowned as a calculating figure, and he has clearly done the maths on the scenario facing his team in the Champions Cup. For tomorrow's match, he has picked only four of the players who started against Toulon.

Not that Warriors coach Gregor Townsend, a former Montpellier player himself, will have read too much into that. "The DNA of Montpellier players is to come and play," he said. "They can be very dangerous.

"They have big names and quality throughout their squad. They have one of the biggest budgets in France and spent the money on top players. Whatever team you have you can only pick within your European squad and their 30-odd players are their best. We expect them to field a strong team."

Publicly, the Glasgow players have stuck to the line that it is all about getting the win, and that they are not thinking about bonus points. Realistically, a fast start and an early score or two would do more than get the job underway, it would also have a dispiriting effect on opponents who have nothing to gain from the match anyway. If Glasgow can play close to the level they did against Bath, when they scored five tries, they can coast it, but they have struggled recently to find the rhythm they had that day.

Townsend was a cosmopolitan animal in his playing days, and you can sense his frustration that Glasgow have made little impact in Europe on his watch. Two seasons ago, they threw away the 15-0 lead they established over Northampton in their opening game, and he admits that they lacked the self-belief then to kick on from such a commanding position. Last season, they lost twice to Cardiff when too many of their players had been jaded by involvement in Scotland's autumn Tests.

That has hardly been a problem for Edinburgh these past two seasons. Yet the capital side has been in splendid form recently, buoyed by turning the tables on Glasgow in the 1872 Cup. There are still many permutations in their Challenge Cup pool, but a win of any kind in Lyon tonight would probably send them through as group winners. Even in the lesser competition, that achievement would represent considerable progress.

"If we win we are in a good position but it is never easy going to France," said Alan Solomons, the Edinburgh coach. "The Top 14 is important to Lyon, but they have depth in their squad and operate big budgets. They have beaten Toulouse, Clermont and Stade Francais. They have picked up some big scalps."