Scotland twice led after tries by the Glasgow full-back - his fifth in three Tests - and Tim Swinson, early in the second half.
But with several injuries to contend with, they had to settle for a bonus point after beating Ireland first up.
"France had a massive forward pack and really brought it to us. I think we chucked it away at the end," said Stuart after the game.
"Our errors cost us throughout the game. We got ourselves in a good position after the first try, but we didn't look after the ball, we didn't respect it enough and ultimately that cost us.
"It wasn't the result we were looking for. Our next job now is Wales in a couple of weeks and we have to get ourselves back on the horse."