Making a rule that hero have to find "someone" to love him back is pretty obvious. Both Fran and mc didn't get love from their parents, so her plan was to FORCE mc to find someone who will truly love him. We also know that mc never had long relationship despite being handsome and popular, so there is something which prevents mc from making strong connection with other people, probably due to his childhood, and mc needs this push from Fran.
Tragic part is that Fran actually suits this requirement, she loves mc and she is an elf, but she's only got 10 days left, so she also don't want to get too close with mc because she will disappear very soon anyway.
As for the part why this person should be specifically an ELF is probably debatable. I would say that Fran simply want to help this specific elf as well and want to achieve these 2 goals at the same time, as she once said mc is the only person who can help Lefi. And another motivation is that she wanted revenge on the other slave trader and this whole scheme helped her get to him.
