Riven is not a great one against Rene. Perfect world Rene will always win the match. He out sustains her, and goes toe to toe damage wise. He has to misplay it badly to lose.
I agree with this. I played as Renek vs. a Riven a few weeks ago. When she tried to initiate with Q or get up close, stun, then combo. I managed to land my fury stun to stop any of her harass. Won that lane easily. As long as she doesn't get the combo off, you should be okay, if not a little vulnerable to ganks.
Insert obligatory "It's over 9000" joke here