However, Lineen's youngsters blunted a France side that had won their last three matches in convincing fashion for much of the clash, losing 18-13.
And with this weekend's trip to Wales representing Scotland's last chance of snatching a Championship victory in 2014, Lineen believes his side are edging closer to their true potential.
"Against a very good French side we showed we're moving in the right direction," he said.
"There are a lot of youngsters in this side, so, from a coaching point of view, this was a satisfying performance.
"Unfortunately, we leaked seven points in front of goal and that's something we must address."