Speaking to the media after the game, the Scotland head coach confirmed that lock Gregor Brown is unlikely to recover in time, while fellow second-row Scott Cummings will also be assessed over the coming days.
"Gregor Brown's got a hamstring issue so I would think he wouldn't turn that round and Scott Cummings is a calf," said the head coach. "Sometimes these can be neural and what they feel is a torn calf or a torn hamstring might not be what we fear but it looks like certainly Gregor will be out and we'll see about Scott over the next few days."
There was more encouraging news regarding wing Kyle Steyn, who impressed again in Scotland's attacking display against the French.
"Kyle Steyn just told me he'll be fine. I hope he's right because he's in a pretty good run of form. He was amazing today again. And the best thing he did, it involved his injury. That hustle back to try to stop a French try. Obviously we were well ahead on the scoreboard but that was great to see. He's got a deep cut, so let's hope it heals."
Townsend also explained the decision to withdraw centre Huw Jones during the match, given the player's previous Achilles problem.
"Huw Jones has obviously had an achilles injury in the past. That's why he missed November. He was feeling it a little bit. He stayed on and then we decided to take him off. I was more reluctant to bring the bench on today just because of the injuries we had. Josh Bayliss was covering the second-row. But given Huw's situation we had to bring him off."
The Scotland coach reserved particular praise for Jack Dempsey, who produced an influential performance after working his way back to fitness.
"I want to mention Jack Dempsey, who not only got himself back to playing this game, a really big game for us, but was outstanding. He probably had his best game of the tournament and doing that while not 100 percent was great to see. I think he'll be fine [for next week]. Today would give him a lot of confidence that he can play a physical game and play 80 minutes. I think the other two might be tougher ones."`