In September of 2350, the U.S.S. Curie, a Starfleet science vessel, was in Spacedock in orbit around Earth, and most of the officers and crew were on leave while the ship was undergoing repairs and refits.
This included Lt. Commander Carol Tiberius Marcus-DeSabel and her husband, Lt. Thomas Vincoer DeSabel. They were staying in Paris with relatives of Tom's: his sister and brother in law, Colleen and Peter Allain.
On the morning of the 21st, Carol gave birth to Jax Kirk DeSabel.
I might as well mention that Carol's parents were David Marcus and Saavik, both of whom I presume you will have heard of.
At that time, children weren't allowed on Starfleet ships. Carol stayed in Paris for five months after Jax was born, but eventually had to return to duty. Jax was left in Paris with his aunt and uncle, Colleen and Peter, as his legal guardians while his parents were away. His godparents were Denise Kallerinth, who was a cousin of Tom and Colleen's; and her husband Jaak Luukarn.
Denise and Jaak were in Starfleet as were Jax's parents, but still, they all saw Jax (and the rest of their family) as often as they could over the years...