Connection data here might imply IP address: "Qwant also collects connection data, not associated with your search queries, only to ensure the security of its information system and, if you create or modify Boards, to respect the obligation to identify content creators such as mandated by French law (article 6-II de la Loi pour la confiance en l’économie numérique)." They also say: "When you search, your query is instantly anonymized by being dissociated from your IP address, in accordance with what the French data controller advices." Dissociated could mean "not stored at all", but it might also mean "stored separately from your search queries".