Yes, they will. All that is needed is for the non-Catholic party to agree to the conditions of the marriage, particularly to raise any children of the marriage as Catholics. As the marriage is between two baptized Christians, it would still be sacramental.
Veronica, the non-Catholic does not make a promise to raise the children Catholic. The Catholic party does.
Can. 1125 The local ordinary can grant a permission of this kind if there is a just and reasonable cause. He is not to grant it unless the following conditions have been fulfilled:
1/ the Catholic party is to declare that he or she is prepared to remove dangers of defecting from the faith and is to make a sincere promise to do all in his or her power so that all offspring are baptized and brought up in the Catholic Church;
2/ the other party is to be informed at an appropriate time about the promises which the Catholic party is to make, in such a way that it is certain that he or she is truly aware of the promise and obligation of the Catholic party;
3/ both parties are to be instructed about the purposes and essential properties of marriage which neither of the contracting parties is to exclude.
Also, in a subsequent post the OP indicates that his fiancee has a prior marriage, so most of this thread has become dedicated to discussing that aspect of the situation. She is not free to marry. She needs to petition for a decree of nullity or a dissolution of the bond. And, the OP’s fiancee is unbaptized therefore if they contract a marriage it will be a natural marriage until such time as she decides to be baptized, only upon her baptism would it become a sacrament.
Also, following Vatican 2, you no longer need a dispensation to marry a non-Catholic.
A Catholic needs a dispensation from disparity of cult to marry an unbaptized person. The Catholic needs permission for a mixed marriage if the non-Catholic is baptized. See these canons:
Can. 1086 §1. A marriage between two persons, one of whom has been baptized in the Catholic Church or received into it and has not defected from it by a formal act and the other of whom is not baptized, is invalid.
§2. A person is not to be dispensed from this impediment unless the conditions mentioned in cann. ⇒ 1125 and ⇒ 1126 have been fulfilled.
Can. 1124 Without express permission of the competent authority, a marriage is prohibited between two baptized persons of whom one is baptized in the Catholic Church or received into it after baptism and has not defected from it by a formal act and the other of whom is enrolled in a Church or ecclesial community not in full communion with the Catholic Church.