So what did Aymeric actually say...

[Lunaxia]

...at the end of 3.2? After Estinogg flew off at the peace conference, he distinctly mouthed something we didn't hear. I always thought there'd be a more significant moment between the two of them on the SoF that might have referred to it, but it ended up having the WoL and Alphinaud as the pivotal characters in those scenes. 3.3 actually ended up far more "happy ending" than I thought it would...

And which parent does "Borel" come from? He seems to be a minor noble of some sort, yet he's supposedly a bastard and not born into aristocracy.

[Enkidoh]

Spoilers ahead of course...

I assumed he said "Death to Nidhogg" which was the same thing the rest of the crowd was chanting, as it made sense, showing how things had rapidly descended into hysteria (and further showed the Warrior of Light and Alphinaud as 'outsiders' to the conflict).

As for Aymeric's surname of de Borel, it's hard to say -

it's not clear if Thordan the VIIth was from either of the four main High Houses, or from a more 'lower' house. The illegitimacy though highly likely came from his mother's side, as it was specifically stated that Thordan as a member of the Church's senior clergy was forbidden to marry (and by extension, bare offspring), it wasn't specifically stated as being a result of either being high born or low born however.

So Aymeric probably took his mother's name as he was forbidden to take his father's name (which would be the source of the rumours about his illegitimacy on it's own, akin to having a big flashing sign above his head saying "Bastard child").

This is just my own theory though so take from it what you will.

Either way hopefully the lore book will go into detail about Aymeric's family origins.