Title holders Munster come next on 6/1 bracketed with Stade Francais - in Pool 4 along with Llanelli Scarlets, Ulster and Harlequins.
Commenting on the draw, Munster team manager Shaun Payne said, "There's not an easy Pool anywhere and perhaps we are in one of the more difficult ones. Getting two French teams was a bit of a stinger.
"We know Clermont Auvergne of course very well from last season. They are going to be immense games, both home and away. There's a lot of history between ourselves and Sale Sharks, while Montauban are an unknown quantity. We will have to do a lot of homework on them."