Brown was dropped from the matchday squad after the 28-6 defeat by Ireland on Feb. 2 and missed the loss to England and win over Italy.
"I think Saturday is a game that will really suit Kelly. Unlike other sides in the competition, France play above the ground a bit and there will be a lot of mauling," Johnson said in a Scottish Rugby Union (SRU) statement.
"I think the pitch suits Kelly too and I've picked a side that can win the game and that's most important."
Brown, who replaced Chris Fusaro, was one of three changes in the pack with prop Geoff Cross starting at tighthead and David Denton coming in for the ill Ryan Wilson in the back row.
15-Stuart Hogg, 14-Tommy Seymour, 13-Alex Dunbar, 12-Matt Scott, 11-Sean Lamont, 10-Duncan Weir, 9-Greig Laidlaw; 8-David Denton, 7-Kelly Brown, 6-Johnnie Beattie, 5-Jim Hamilton, 4-Richie Gray, 3-Geoff Cross, 2-Scott Lawson, 1-Ryan Grant
Replacements: 16-Ross Ford, 17-Alasdair Dickinson, 18-Euan Murray, 19-Tim Swinson, 20-Ryan Wilson, 21-Chris Cusiter, 22-Duncan Taylor, 23-Max Evans
- Geoff Cross
- David Denton