Fei, as Id, is trying to kill Elly when they are both in their gears, fighting above Yggdrasil. Moving in for the kill, he gets grabbed by Elly, and he demands that Elly let him go. Elly responds with "Fei... I won't ever let go!" She manages to turn him back into Fei.
He pays her back at the end of the game by chasing Deus through the atmosphere while calling her name, then getting into a debate with Krelian's giant floating head, and going toe-to-toe with the last remnants of Miang to win her back, and it works.
Let's not forget the hidden scene in the lighthouse where we see 1)the story of Emeralda's creation and 2)Emeralda being hugged by her "father" and willing herself to grow up so she can be more helpful to him.
Even before this, Emeralda's giddy fit after recognizing Fei for the first time in 4000 years is adorable, especially since she's normally so reticent.
After the scenes in Zeboim, go back to Citan's house. Remember that music box Citan showed Fei near the beginning of the game? The one that had been excavated from some old ruins? The one that Fei said the music sounded familiar? Check the side of the box...
"Celebrating my daughter's birth... may all the dreams, courage & love in the world be yours..."
After the final confrontation:
Elly: Will we make it in time?
Fei (holds out his hand): Can you run?
Elly: If we're together, I can. (takes Fei's hand)