Canon (Church) law after Gratian (12th century) set the lower limits on marriage to 12 for girls and 14 for boys. Canon law recognized consent, NOT consummation, as the deciding factor of a valid marriage. In practice, lack of consummation could and did sometimes function as an excuse to dissolve a marriage that was no longer politically expedient (for the nobles involved, but also for the Church, since they still needed ecclesiastical approval). In 16th century France, Jeanne d'Albret's first marriage was annulled for lack of consummation.

On the diversity of "average age at marriage" in medieval Europe, you might be interested in this earlier answer.