The Top 14 side managed to grind out a hard-fought 9-6 victory over the Warriors - Rory Kockott landing three penalty goals - but have to take all the match points on offer in Sunday's second leg at the Stade Pierre Antoine.
Castres will have to manage to do something they have failed to do so far in this campaign and that is score a bonus point victory against a Glasgow side still looking for its first win.
Castres will be aware Northampton Saints, who play Ulster in Ravenhill, are only two points behind them in the table and that will make a comprehensive win over Glasgow pivotal to their cause.
Glasgow, like their Scottish counterparts Edinburgh, have failed to engineer a win in this season's Pool stages so far but they have managed a solitary losing bonus point for their efforts
• Glasgow have managed just two clean breaks in three matches, a joint-low in the tournament.
• Glasgow have a 24% win rate in 25 previous matches in this tournament against French opponents (W6 D2 L17).
• Away from home, the Glasgow have mustered only four wins from 41 attempts (D1 L36), only one of these coming against a French side (Toulouse in 2009, 33-26).
• A third successive victory for Castres would be their best winning run in the tournament since the 2001/02 season, when they won six straight matches.