A Catholic person must celebrate their marriage in the Church. They must be married in the Church, if they are not married in the Church and have not received permission or a dispensation from the local bishop, then the marriage is invalid, and they are living in adultery. As a result, they cannot receive Holy Communion.
If there are valid reasons preventing a canonical wedding in the Church, the person should seek permission from their bishop. In serious cases, the bishop may grant a dispensation and recognize a marriage that was performed civilly. Alternatively, the bishop can also perform a "sanation in the root" through a decree, recognizing the civil marriage.
However, this must always be done with the permission of the Church.