Matthews (Orica-GreenEDGE), who won the eight-day race's prologue on Sunday, added to his overall lead with two bonus seconds in the final 15km to keep the leader's yellow jersey ahead of Tom Dumoulin (Giant-Alpecin) and Patrick Bevin (Cannondale).
"It was a hard day all day. But I'm glad we had a super strong Orica team today to take care of the race and bring back the four escapees," Matthews said.
"The main focus today was on defending the jersey. It would be nice to win a stage but the jersey was the main focus.
"It's great to hold it for one more day especially as I managed to take two seconds in the last intermediate sprint. The final lap was tougher than I expected.
"I saw that some of the GC guys were up there so I had to make the effort to chase them. Maybe it took away some of my energy for the sprint."
Demare (FDJ) was the strongest in the final stretch leading to the finish line in the streets of Vendome and won ahead Ben Swift (Sky) and Nacer Bouhanni (Cofidis).
The 198km ride from Condé-sur-Vesgre to Vendôme started under snowflakes after a minute's silence in memory of French rider Romain Guyot, who recently died in a training accident.
"I'm super happy. It was a hard day with the snowflakes. It was tiring, especially the little lanes in the finale," Damare said.
"We were not that many in the end. It's a victory I had been waiting for for a long time. The team did a good job. Everybody is smiling.
"Last year was a struggle and it's nice to be able to prove I can still win a big one. For me, the last big one I won was my French title in 2014. In the days ahead, it will be different.
"It was not a normal sprint today. I launched it from afar. I had decided to focus on Nacer (Bouhanni) as he had two team-mates left with him.
"I was lucky to be able to overtake him in the last stretch and to retain enough strength to upstage Swift. There is no petty rivalry between the French. I'm glad to win against anyone."
Thomas De Gendt (Lotto-Soudal), Perrig Quemeneur (Direct Energie), Steven Tronet (Fortuneo Vital Concept) and Theirry Houpond (Delko Marseille Provence) set the pace with a 10min lead on the peloton.
The quartet were later caught by a reduced peloton which split due to high winds and the cold conditions.