I could list a hundred thousand, really, but here are some childhood headcanons-
Mrs. Potter was such a lady, okay. Sometimes she would get a prim look on her face, pretending to be affronted when James did something particularly ungentlemanly, but her eyes-always warm-gave her away every time. She was very warm and loving person, and even her scoldings never lasted for long. Mr. Potter was tall, if a bit portly in his advanced age. He smoked all time and had a contagious laugh. He would rant on and on about social issues, he abhorred blood supremacy and complacency. James inherited his mother’s hazel eyes and his father’s messy hair and a good nature from them both.
They were either semi-retired when he was born or didn’t work in the first place. Either way, they spent as much time with him as possible. They generally adored him and he grew up very well loved and cared for, which is actually pretty canon.
They took great care to educate him properly. The spoke about muggleborn rights, about magical creatures of all kinds, but more so that prejudice is born of ignorance. They were far more concerned that James understand the reasoning behind his beliefs and be able to justify them with sound logic. They taught him to question things, even authority, and that the right thing to do isn’t always inside the parameters of the law. I envision long tirades about corruption in the wizarding world and how the system and society is broken and I love it, ok?
His worst punishment was for flying his broom in the house when he was six. That by itself would have been fine, but he whipped around a corner and knocked his grandmother clean on her arse. His mum thought it was actually a bit funny, but had to prove a point. She confiscated his broom for the entirety of his grandmother’s stay. It was the longest three weeks of his childhood.
The Potters had a large library, stocked with both wizarding and muggle literature and non-fiction books. James grew up reading muggle philosophy books and adventure stories right along with early magical education. His parents brought in tutors for specific subjects, but Mrs. Potter had a very strong hand in his education.
He grew up in a manor house-which is cliché, but also very plausible given the loads of money Harry inherited and that the Potters were an old pureblood family. When James was seven, he accidentally discovered a secret passage on the second floor. He was so startled and excited by this discovery that he went to get his dad at once. His father then sat down and showed him an old tattered leather book, which was actually a field book documenting his own childhood explorations of the house and grounds. Mr. Potter gave James a similar book, a muggle torch, and a knapsack, and a clue to get him going. He set off in earnest to explore and map out the entire grounds, just like his father had done. He kept a daily log in his book and he would compare notes with his father after supper each night. Mr. P would set him up for new adventures, and reward him for each discovery with a clue to something even better. It took him the better part of two years, but he did it.
His parents took often James to classic theatre in London. He hated operas and loathed ballets, but adored anything a with a sword fight.
Both of his parents let him use their wands, teaching him random spells and always told James don’t-tell-your-mum or don’t-tell-your-dad. They both actually knew about this, of course, but loved it when James felt like he was getting away with something.