Forrest is undaunted by the size of the task, but he also says the six times European champions "pose a threat all over the pitch".
"We want to progress as far as possible," Forrest told BBC Sport Scotland.
"Our challenge is to go and win trophies. Every competition that we play in, we want to go and win it. We believe we can with the squad we've got.
"We've won our first game [at Sale] of the pool and winning away from home is obviously a big thing. But for us, and any team that wants to progress in European competition, you've got to win your home games.
"We'll shine a light on that, but any team coming to Scotland know it's on the plastic pitch, there is a full crowd behind us and it is going to be tough for them."
France skipper and superstar scrum-half Antoine Dupont is just back from a long-term injury, and may be rested for Saturday's meeting but Toulouse carry threats all over the pitch including Scotland full-back Blair Kinghorn and a monster forward pack.
"It's a big challenge. But we also know that Scotland is a very hard place for other teams to come and play," he added.
"We don't lose many games at home. It's probably one of the toughest challenges we're going to get, and it would obviously be a massive result.
"Off the back of Friday night, winning away from home [Sale], to then back that up at home against a team like Toulouse, it would be pretty big.
"Toulouse are a quality team. They've got a really strong history in the competition, they're littered with quality international players, but then you could say the same about us.
"It's a one-off game and in a one-off game, we're pretty confident that if we get things right, at home, it could be a pretty special night."