I'd have to brush up on my anime openings and endings, but this is how I would imagine what kind of songs would be in.
The opening of Season 1 would be something energized and upbeat, something akin (not exactly) to the One Piece and Fairy Tail first OPs. The first season was mostly systematic and not changing majorly in plot, so the song should reflect that season's naiviety and lightness. As for the ending, I think it would be a bit more easygoing and slow, maybe a song about the main duo's feelings for each other.
We don't know much about Season 2, but it's supposed to be bigger on story and characters. I think the opening song would still be high-energy, but it would take on a more serious tone. Through in some imagery of the new heroes, new villains, and the darker emotional plot going on with Hawk Moth, and it could be a very energizing yet question-raising opening song. The ending could be very somber with a touch a hope. It could easily be a song reflecting of the effect of Mrs. Agreste's disappearance, or it could be about the heroes, old and/or new, struggling with their confidence to be the heroes.