Scotland started strongly at The Hive and took a lead into half time courtesy of a first international score for hooker Elis Martin following a rolling maul.
The hosts dared to dream of a first win over France in this Championship since 2010 but Les Bleues hit back after the interval and went ahead when Arbey crossed in the right-hand corner.
The match remained in the balance until the very final act, when replacement Gros walked in from close range to ultimately settle a hard-fought clash and deny Scotland what would perhaps have been a deserved losing bonus point.
MARTIN GIVES SCOTLAND ADVANTAGE
Scotland started strongly in front of a raucous crowd of more than 5,000 but were unable to make a couple of promising early lineout positions count, with the set piece going awry.
Romane Ménager was first to threaten for France, the No.8 storming clear from the back of a ruck on the halfway line and making it to within five metres before she was tackled.
France passed up the attacking lineout that followed but it did not take them long to go in front, Lina Queyroi slotting over a penalty after a deliberate knock-on.
Helen Nelson, so good off the tee in Scotland's win over Wales in Round 1, spurned a presentable opportunity to immediately level matters after fine work by Evie Gallagher at the breakdown and the hosts had to show their defensive mettle for a sustained spell thereafter.
Nassira Kondé knocked on when well placed on the right wing and Assia Khalfaoui was held up as the visitors were frustrated by a stubborn Scottish wall.
Having survived pressure on their own line, Scotland ended the half by applying their own at the other end of the field.
The home pack were held up a couple of metres short first time around but there was no stopping them when they were handed another opportunity soon afterwards.
The lineout was this time executed perfectly and hooker Elis Martin was on hand to apply the finishing touch and mark her first Scotland start with a score.
Nelson dragged the conversion wide but Bryan Easson's side held their lead until the break.
ARBEY TURNS ON THE STYLE
Scotland made an inauspicious start to the second half when Meryl Smith spilled a clearance kick into touch and France almost made them pay straight away.
The ball was swiftly moved through the hands and Emilie Boulard was denied by a fine tackle from Rhona Lloyd which kept Scotland in front.
Kelly Arbey spilled a Kondé knock-on when she may have had the line at her mercy but there was no stopping the teenage wing in the 52nd minute.
A typically flowing French move ended with Boulard drawing the last defender and finding Arbey, who kept her footing after an attempted tackle and dotted down.
The conversion was missed, keeping the lead at just three points, but Scotland were unable to make serious inroads and instead had to dig in to stay in the contest.
Gallagher earned another vital turnover five metres from her own line with 10 minutes to play before Lisa Thomson gave the hosts hope with a penalty which gave them rare field position.
But the French pack, bolstered by the fresh legs of their replacements, forced their opponents back at the lineout and soon earned a penalty of their own to ensure they could see out the final moments deep in Scottish territory.
They were initially kept at bay but with the clock in the red, a gap opened up for Gros to seal the outcome, with Queyroi's kick bringing an end to a tense encounter.