Vernon, 22, who won at the Challenge Mallorca to start the season, took advantage of a shambolic long-range free-for-all sprint in the finale to also snatch the overall lead.
Most of the pure sprinters had been dropped in an early attack over two hills led by the Ineos team, with British veteran Mark Cavendish pulling out with 60km to go.
Cavendish's team leader Aleksandr Vlasov also pulled out ahead of the start due to Covid-19.
Another Briton, Simon Yates, withdrew during racing because of stomach problems. The leader of the Australian outfit Jayco-Alula had been a contender for the overall title.
The sprinters in the second part of the peloton appeared to get lost and somehow go the wrong way before local police stopped them and sent them in the right direction.
Thursday's stage is also a hilly run featuring five categorised climbs between Morteau and La-Chaux-de-Fonds.
