The 31-year-old Martin, who was on his own during the final stretch of the 181-kilometer (112-mile) stage, clocked a time of 4:13:43, reports Efe.
France's Pierre Latour, of Ag2r La Mondiale, finished in second place, followed by Spaniard Alejandro Valverde, of Movistar, in a stage that started in Brest and ended in Mur-De-Bretagne Guerledan.
Belgium's Greg Van Avermaet, of BMC, retained the overall yellow jersey, while Briton Chris Froome, of Sky, the defending champion, is one minute and two seconds off Van Avermaet's overall lead.
Friday's 231-kilometer seventh stage will take the cyclists from Fougeres to Chartes.
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