Money deposited in Anytime accounts is isolated from the company's cash flow. If Anytime were to go bankrupt, your funds would be returned to you in full, as they are ring-fenced in the books of Crédit Mutuel Arkéa or Société Générale. This means that no one but you has access to your money. Neither Anytime nor anyone else.
In the event of bankruptcy of Crédit Mutuel Arkea or Société Générale, funds deposited in these banks are guaranteed by the Fonds de Garantie des Dépôts et de Résolution (FGDR) up to €100,000 per customer. The risk of these two banks going bankrupt is unlikely: they are the largest banking groups on the French market.