Frane went ahead after less than a minute when Lyam Akrab powered over, with Jean Cotarmanac'h converting.
Scotland responded within six minutes through a try fromfull-back Jack Brown with Matthew Urwin converting.
France lost number eight Antoine Chalus-Cercy to a yellow card - which really should have been red - for a high tackle during the build-up.
The hosts scored next through Akrab while scrum-half Baptiste Tilloles, centre Oliver Cowie and Echegaray also went over for the hosts before the end of an entertaining first half along with Scotland wing Fergus Watson and prop Ollie Blyth-Lafferty as the hosts led 33-22.
An Urwin penalty and a superb finish from replacement Cameron van Wyk either side of another Echegaray touchdown reduced the gap to eight points.
Fly-half Cotarmanac'h converted his own try to give the hosts some breathing space, but Scotland captain Freddy Douglas barged through two tackles to score and Brown's conversion increased the home nerves.
Scotland piled on the pressure as the clock ticked down and smart work from the Scots saw Urwin take the three points from a drop goal knowing a converted try would not be enough.
It gave the visitors the chance to snatch an incredible victory from the restart, but the hosts won a penalty to end the match and kick-start their celebrations.