Froome finished 22nd in Saturday's 191-kilometer (119 mile) ride from Saint Pourcain-sur-Sioule to Lyon but maintained a 2 minute, 28 seconds lead in the overall standings over Bauke Mollema of the Netherlands.
Alberto Contador of Spain was third overall heading into Sunday's Stage 15, a Bastille Day odyssey that covers 242.5 kilometers heading into the mountains.
"There is still everything to race for at this point; 2 1/2 minutes is nothing when you have a bad day in the mountains," said Froome. "I just hope to get through the Alps without any bad days and get a bit closer to Paris."
Trentin bolted to the lead and edged Switzerland's Michael Albasini and American Andrew Talansky at the line with a winning time of 4 hours, 15 minutes, 11 seconds.
"I waited until the 200-meter to go mark to launch my sprint because we had a tailwind so it was good," said Trentin. "It's my first (stage) win as a pro, a nice way to start."