A spectacular second-half implosion against Wales and a 44-8 thrashing by England had left France without a win after two games. However, tries by Ntamack, Yoann Huget and Gregory Alldritt (2), and five points from the boot of Thomas Ramos as well as a Baptiste Serin conversion restored some pride for Les Bleus.
Scotland had only Greig Laidlaw's first-half penalty and a late Ali Price try converted by Adam Hastings to show for themselves.
France, who had lost 10 of their previous 13 matches under coach Jacques Brunel, next travel to Ireland with Scotland hosting Wales.
Wales crowned Six Nations champions as Scotland beat France
Brunel gave hope to a weakened Scotland by fielding Ntamack, who usually plays centre, at flyhalf in yet another halfback combination after the coach had omitted Morgan Parra and Camille Lopez following their veiled criticism of the management after the Twickenham rout.
But the 19-year-old Ntamack, paired with scrumhalf Antoine Dupont, produced a sterling performance in Brunel's seventh halfback pairing in 14 tests, with Thomas Ramos winning his first start at fullback.
La joie des Français après l'essai de Romain Ntamack contre l'Ecosse
Image credit: Getty Images
Scotland, who had not won in Paris since 1999, had been forced to make changes to their line-up with Finn Russell, Stuart Hogg and Willem Nel ruled out injured.
In a packed Stade de France on a spring-like afternoon, France started aggressively while Scotland were their usual playful selves.
After a long spell of domination, Les Bleus went ahead when Ntamack touched down at the end of a brilliant move.
They had their second try disallowed because of an earlier knock on after Gael Fickou went over the line following a clever chip from Ntamack.
The hosts lacked discipline but Scotland had only one Greig Laidlaw penalty on the scoreboard at halftime.
A Mathieu Bastareaud chip-and-collect kick tore the visitors defence and Huget finished the move to give France a perfect start to the second half.
The intensity went down but France, who had failed to win six of the last eight times they held a halftime lead, stayed focused and kept their composure.
A third disallowed try was quickly followed by a valid one by Alldritt.
With less than five minutes left, France were sitting on a 17-point cushion, leaving Scotland with no hope of a comeback as Ntamack was replaced after a man-of-the-match display.
The visitors, however, finally scored a try by Price, who made a bee-run to the line to reduce the arrears.
But France continued to play after the clock stopped to get a bonus point when Alldritt touched down again.
France deny Wales Grand Slam in frantic finale
Scotland produce record-breaking win over Italy