Froome will wear the race leader's yellow jersey for a British record 15th day on Tuesday's fourth stage.
The Team Sky rider, 30, finished just behind Spain's Joaquim Rodriguez at the end of a stage marred by two crashes that saw the race briefly stopped.
Overnight leader Fabian Cancellara completed the race after falling but later joined five others in abandoning.
The Swiss rider was thrown head-first into a ditch in the first crash and had lost nearly 12 minutes to his rivals by the time he reached the stage finish.
It was later confirmed he suffered two fractured vertebrae in his lower back after somersaulting over his handlebars as his yellow bike cartwheeled off the road in a spectacular crash about 60km from the finish.
The pile-up was sparked by William Bonnet sliding off, and the Frenchman also abandoned, along with Australia's Simon Gerrans, South African Daryl Impey, Dutchman Tom Dumoulin and Dmitry Kozontchuk of Russia.
The race was neutralised by race directors, meaning the riders continued at a sedate pace to allow those caught up in the crash to catch up.
However, with all doctors at the race tending the wounded, the race was eventually stopped, around 50km from the finish.
