The short answer is “it depends”.
Presuming they have no prior marriages and their own former denomination did not have any requirements for the “form” of marriage-- or they followed the required form, for example in the Orthodox Church-- then their marriage is valid and there is nothing else that they need to do in order to join the Church nor is there anything they need to do to make their marriage valid.
If they were both baptized already their marriage would be both valid and sacramental. If neither were baptized, or one was baptized and the other unbaptized, and they both subsequently become baptized then their marriage becomes a sacrament.
OTOH, If a couple had prior marriages/divorces or other circumstances, these would have to be resolved BEFORE either of them could be received into the Church. And, yes, that would include ceasing relations and could also include a Tribunal investigation and decree of nullity.
