The “unity candle” is not a required element of the Catholic nuptial liturgy, either within Mass or outside of it. The unity candle is a wedding-industry fad of recent decades that has been incorporated into many Christian weddings, Catholic and non-Catholic. Although this groom may have seen this custom performed in weddings at his church, the unity candle is not required in Protestant weddings.
The priest is within his authority to disallow the custom at weddings he witnesses. The couple should understand that it is the sacrament of matrimony that signifies their marital unity, and in fact accomplishes what it signifies. If they like, they can light a unity candle at their wedding reception.