Farrell, who has 104 caps and has been England captain since 2019, drops to the bench with prop Ellis Genge set to lead an otherwise unchanged team that beat Wales 20-10 in Cardiff in the previous round.
Dispensing with the twin playmaker role that former coach Eddie Jones had hoped would come good, Borthwick said starting Smith at flyhalf from the start was the right call against France, with Farrell available to come on towards the end.
"I've said that Owen will captain the team when he comes onto the pitch ... I can't praise Owen enough. Not just for this week, but every day since we started working together in this capacity," Borthwick said.
"He's been incredible at helping all the players around the squad and he cares so much about this team. He has incredible respect from everyone.
"Congratulations to Ellis Genge who will captain the side for the first time. Ellis will lead from the front with the sort of dedication and spirit that now rightly typifies this England team."
Smith was initially released from Borthwick's training squad last month to get game time with his Premiership side Harlequins.
He impressed in a 40-5 win over Exeter Chiefs last Saturday and he is set for his first England start since their opening-round defeat by Scotland.
"Marcus played very well in that game, but this is not his first start this Six Nations. Having players of such ability and talent to select from is a real privilege for me," Borthwick added.
"I'm constantly watching the players in every game they play. Marcus played and trained really well.
"We want to keep progressing ... We speak a lot about how we want to move forward as a squad. Different weeks you play different roles, all the time we're trying to develop the team."
Maro Itoje and Ollie Chessum are at lock while the pack is completed by flankers Jack Willis and Lewis Ludlam, with Alex Dombrandt at number eight.
Jack van Poortvliet is at scrumhalf while Ollie Lawrence is at inside centre and Henry Slade slots in at outside centre.
England are third in the standings after three matches, five points behind leaders Ireland who host Borthwick's side in the final round.
15. Freddie Steward, 14. Max Malins, 13. Henry Slade, 12. Ollie Lawrence, 11. Anthony Watson, 10. Marcus Smith, 9. Jack van Poortvliet; 8. Alex Dombrandt, 7. Jack Willis, 6. Lewis Ludlam, 5. Ollie Chessum, 4. Maro Itoje, 3. Kyle Sinckler, 2. Jamie George 1. Ellis Genge
Replacements: 16. Jack Walker, 17. Mako Vunipola, 18. Dan Cole 19. David Ribbans, 20. Ben Curry, 21. Alex Mitchell, 22. Owen Farrell, 23. Henry Arundell