This quote is usually attributed to Jean-Baptiste Alphonse Karr. As his name suggests, he is French. He was a critic, a novelist, and a journalist. He was born in Paris, and many of his works are autobiographical. His first novel was his first claim to fame. It’s titled “Sous Les Tilleuls”. His original phrase for “the more things change, the more they say the same” is “plus ca change, plus c’est la meme chose”.
It actually translates to “the more it changes, the more it’s the same thing”. The translation that is usually used is the one quoted in this question though. This is one of his little epigraphs, and they’re quoted quite a bit in modern day, so there’s reason to study them.