Despite the probable zoonotic origin of SARS-CoV-2, only limited research efforts have been made to understand the role of companion animals in SARS-CoV-2 epidemiology. According to recent serological prevalence studies, human-to-companion animal transmission is quite frequent, which led us to consider that the risk of SARS-CoV-2 transmission from animal to human, albeit negligible in the present context, may have been underestimated. In this study, we provide the results of a prospective survey that was conducted to evaluate the SARS-CoV-2 isolation rate by qRT-PCR in dogs and cats with different exposure risks and clinical statuses. From April 2020 to April 2021, we analyzed 367 samples and investigated the presence of SARS-CoV-2 RNA using qRT-PCR. Only four animals tested positive, all of them being cats. Three cats were asymptomatic and one presented a coryza-like syndrome. We describe in detail the infection in two cats and the associated clinical characteristics. Importantly, we obtained SARS-CoV-2 genomes from one infected animal and characterized them as Alpha variants. This represents the first identification of the SARS-CoV-2 Alpha variant in an infected animal in France.