This practice is technically possible. However, for security reasons, we strongly advise you NOT to ask your customers to communicate you their own card number.
This practice increases among other things, the risk of dispute on credit card payment, since your buyers will have no track of their purchases in their mailbox. Furthermore, they will tend to forget to what corresponds the payment because they won't have done their credit card's number themselves.
We recommend you to consult the CNIL's advice on that matter in their website: https://www.cnil.fr/en/home.
Instead of taking credit cars over the phone, we propose you as an alternative to use our Payment Requests. This is simply requests sent by email or SMS, and including a link towards a PayPlug secured payment page. (More information)