"When I get home I'm going to bed. Really tired. With you?" he wrote before pressing "send" on Wednesday to his almost 15,000 followers.
Realising his mistake the minister quickly deleted the message ten minutes later, but not before it had been retweeted around the web, with much commentary.
"When Eric Besson proposes going to bed, it's to 13,000 followers. That beats DSK" said one of his followers in a reference to the former IMF boss Dominique Strauss-Kahn.
The intended recipient of the message is not known, although it was probably his wife, Yasmine Tordjman.
Eric Besson suffered a very public falling out with his ex-wife Sylvie Brunel, who published a book in which she dubbed him a 'serial cheat with inter-changeable mistresses'.
Rumour has it that at his marriage to Brunel, Besson stopped the mayor and struck "fidelity" from his wedding vows.
The 53-year-old minister married Tordjman, a 24-year-old art student from Tunisia in September 2010.
The accident was made funnier by the fact that Besson also serves as the minister for the digital economy.
The minister saw the funny side, sending another message saying "LOL and apologies. That will teach me not to go through my draft messages and press send by mistake. I'm not sleeping…"
Much mirth continued online about the message, with copycat tweets springing up on the social network.
The minister eventually tired of the merriment, signing off with "Right, I'll leave you to your silliness. I have a meeting in parliament to prepare…"