We compare test results of SARS-CoV-2 positive patients, depending on their vaccine status, the presence of symptoms and whether they are infected by the Delta variant or not, using a large number of PCR tests done in the community in France from 14 June 2021 to 30 July 2021. In asymptomatic individuals, Ct values at the first positive test were higher in fully vaccinated individuals (> 2 weeks after final dose) than non fully vaccinated individuals (1.7 [1, 2.3], p < 1e-6). In symptomatic individuals however, Ct values at the time of symptoms were not significantly different in vaccinated compared to unvaccinated individuals (p = 0.26). This was true both for infections by Delta and non-Delta (essentially Alpha in France at the time) variants. These results imply that some infected vaccinated individuals, especially if symptomatic, may transmit the virus as much as unvaccinated individuals.