New Zealander Marsh is the man responsible for the rigging on board the French team's boat and when their mast broke last week he injured himself badly after climbing up to cut away the main sail.
He could have left the boat during their pit stop for repairs in Punta del Este in Uruguay but opted to stay to see the team over the line with their hastily patched-together mast and rigging.
"I knew the injury was serious and when I climbed down to the deck I was in shock," Marsh said.
"The guys looked after me very well but when they told me they were going to use a staple gun on me I think I went into shock for a second time.
"It was my decision to stay on board. I'm responsible for the rigging and I didn't want to leave the guys to have to deal with that on their own."
Groupama's third place finish was a remarkable recovery after losing their mast six days ago.
They move back into second place overall, 20 points behind leaders Telefonica. With 30 points available for first place in each of the remaining four offshore legs they still have a realistic chance of victory.