Alongside a romantic picture of the couple embracing on a beach at sunset, Khloé wrote, "Happy birthday baby boy! In only a short amount of time we have created timeless memories.
"Happy birthday to a man who genuinely lives life to the fullest."
She continued, "What's understood doesn't need to be explained. I can't wait to celebrate with you tonight! You deserve it!"
Khloé, who celebrated her 30th in June, started dating French in April, but the couple ended their relationship in September. The pair have remained close, however.
French has been noticeably present at Kardashian family events – most recently attending Kendall Jenner's intimate 19th birthday celebrations – and Khloé has spoken openly about their connection.
"We all miss French. We love French," Khloé told E! News earlier this month. "I'm still friends with him. I still talk to him every day."
French, meanwhile, told US Weekly, "She's my baby forever. She's good. She's the best. There's no bad blood with her.
"I love how she is. She inspires me as a person. I'm sure I inspire her in many different way. We just have that special relationship. Right now we're in a special zone… She's a beautiful person. I don't think a lot of people know how beautiful she is."