After its first description in Wuhan (China), SARS‐CoV‐2 the agent of coronavirus disease 2019 (COVID‐19) rapidly spread worldwide. Previous studies suggested that pets could be susceptible to SARS‐CoV‐2. Here, we investigated the putative infection by SARS‐CoV‐2 in 22 cats and 11 dogs from owners previously infected or suspected of being infected by SARS‐CoV‐2. For each animal, rectal, nasopharyngeal swabs and serum were taken. Swabs were submitted to RT‐qPCR assays targeting 2 genes of SARS‐CoV‐2. All dogs were tested SARS‐CoV‐2 negative. One cat was tested positive by RT‐qPCR on rectal swab. Nasopharyngeal swabs from this animal were tested negative. This cat showed mild respiratory and digestive signs. Serological analysis confirms the presence of antibodies against the SARS‐CoV‐2 in both serum samples taken 10 days apart. Genome sequence analysis revealed that the cat SARS‐CoV‐2 belongs to the phylogenetic clade A2a like most of the French human SARS‐CoV‐2. This study reports for the first time the natural infection of a cat in France (near Paris) probably through their owners. There is currently no evidence that cats can spread COVID‐19 and owners should not abandon their pets or compromise their welfare.