Background Since 2005, cases of chikungunya (CHIK) were caused by an unusual vector, Aedes albopictus. This mosquito, present in Europe since 1979, has gained importance since its involvement in the first CHIK outbreak in Italy in 2007. The species is capable of transmitting experimentally 26 arboviruses. However, the vectorial status of its temperate populations has remained little investigated. In 2010, autochthonous cases of CHIK and dengue (DEN) were reported in southeastern France. We evaluated the potential of a French population of Ae. albopictus in the transmission of both viruses. Methodology and Principal Findings We used two strains of each virus, CHIK and DEN: one strain was isolated from an imported case, and one from an autochthonous case. We used as controls Aedes aegypti from India and Martinique, the source of the imported cases of CHIK and DEN, respectively. We showed that Ae. albopictus from Cagnes-sur-Mer (AL-CSM) was as efficient as the typical tropical vector Ae. aegypti from India to experimentally transmit both CHIK strains isolated from patients in Fréjus, with around 35–67% of mosquitoes delivering up to 14 viral particles at day 3 post-infection (pi). The unexpected finding came from the high efficiency of AL-CSM to transmit both strains of DENV-1 isolated from patients in Nice. Almost 67% of Ae. albopictus AL-CSM which have ensured viral dissemination were able to transmit at day 9 pi when less than 21% of the typical DEN vector Ae. aegypti from Martinique could achieve transmission. Conclusions/Significance Temperate Ae. albopictus behaves differently compared to its counterpart from tropical regions, where recurrent epidemic outbreaks occur. Its potential responsibility for outbreaks in Europe should not be minimized.