Brown will become the 43rd Scotland player to reach 50 caps when he lines up against Les Bleus, while Grant Gilchrist and Nick Haining are the other two changes to the pack.
Meanwhile, Duncan Weir could make his first Scotland appearance since the 2017 Championship after the 27-cap fly-half was named on the bench by Gregor Townsend.
British & Irish Lion Stuart Hogg remains at full-back in an unchanged backline which sees Chris Harris and Sam Johnson in midfield as Adam Hastings and Ali Price resume their half-back partnership.
Townsend said: “This week we face a France team that looks galvanised since the World Cup, with a potential Grand Slam in their sights following impressive wins over England, Italy and Wales.
“We have a lot of respect for their coaching team and the quality of player they possess throughout their squad, many of them just in their early stages of their international careers.
“We’re going to have to deliver our best rugby of the Championship in order to beat a team in such good form. Coming back to BT Murrayfield is always a very special feeling.
“The energy generated from the Scotland supporters means a great deal to everyone associated with the squad. Our players are looking forward to revelling in that atmosphere on Sunday.”
Elsewhere, Sam Skinner has recovered from injury to take his place on the bench for the first time in this campaign, where he is joined by Magnus Bradbury and Stuart McInally.
The remainder of the pack is unchanged as Zander Fagerson, Rory Sutherland, Scott Cummings, Jamie Ritchie and Hamish Watson start their fourth consecutive Test.
Scotland team to play France at BT Murrayfield Stadium:
15. Stuart Hogg (Exeter Chiefs) – 75 caps – Captain
14. Sean Maitland (Saracens) – 47 caps
13. Chris Harris (Gloucester) – 17 caps
12. Sam Johnson (Glasgow Warriors) – 12 caps
11. Blair Kinghorn (Edinburgh) – 20 caps
10. Adam Hastings (Glasgow Warriors) – 19 caps
9. Ali Price (Glasgow Warriors) – 31 caps
1. Rory Sutherland (Edinburgh) – 6 caps
2. Fraser Brown (Glasgow Warriors) – 49 caps – Vice captain
3. Zander Fagerson (Glasgow Warriors) – 28 caps
4. Scott Cummings (Glasgow Warriors) – 11 caps
5. Grant Gilchrist (Edinburgh) – 41 caps
6. Jamie Ritchie (Edinburgh) – 17 caps
7. Hamish Watson (Edinburgh) – 31 caps
8. Nick Haining (Edinburgh) – 2 caps
16. Stuart McInally (Edinburgh) – 36 caps
17. Allan Dell (London Irish) – 31 caps
18. Willem Nel (Edinburgh) – 37 caps
19. Sam Skinner (Exeter Chiefs) – 6 caps
20. Magnus Bradbury (Edinburgh) – 13 caps
21. George Horne (Glasgow Warriors) – 12 caps
22. Duncan Weir (Worcester Warriors) – 27 caps
23. Kyle Steyn (Glasgow Warriors) – uncapped