On France's Bastille Day, fellow Frenchman Sandy Casar placed second, 57 seconds behind Moncoutie's winning time of 4:20.06, while two other Frenchmen, Patrice Hagland and Franco Pellizotti, finished fourth and sixth, respectively.
Rasmussen was also in the main pack and placed 46th, while France's Christophe Moreau remains third following a 44th-place performance.
Belgian Tom Boonen, who was the race's sprint points leader, withdrew from the race after injuring his right knee in a crash Wednesday.
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