Edinburgh, who ended their seven-game losing streak in the RaboDirect PRO12 with a 26-23 victory over Scarlets on Friday, will be underdogs in the quarter-final against the four-time winners but Bradley believes the home faithful have a big role to play.
Having seen off the likes of London Irish and Racing Metro 92 in the group stages, the Gunners have the chance to put a disappointing domestic season behind them in what Bradley is billing as one of the biggest games in the club's history.
A win against the Top 14 side would see Edinburgh progress to their first ever semi-final in the competition, but Bradley isn't getting carried away.
He said: "There's no question that Toulouse, the four-time champions and arguably the biggest name in European rugby, will pose a massive challenge.
"With less than a week to go the anticipation is really starting to mount for this very exciting, and very significant, match in Edinburgh Rugby's history.
"We can't thank our fans enough for the overwhelming support shown for this fixture, it's going to be tremendous day, with lots happening in and around the ground to bring the stadium to life.
"That's why we need every voice we can muster out there on Saturday, screaming on our boys for 80 minutes by coming decked out in black and red, banging drums, waving flags, swinging scarves and singing songs.
"Anything they can do to ensure every supporter plays their part in making the most of home advantage will be crucial."
63x46.png){kind=logo}