"By the time you receive this letter, I will be dead," Baudelaire wrote to his mistress Jeanne Duval when he was 24. "I am killing myself because I can no longer live or bear the burden of falling asleep and waking up again."
But he went on to live another 22 years.
He did stab himself in June 1845 but failed to do any serious damage.
Had he succeeded he would never have written his best-known collection of poems, Les Fleurs du mal (The Flowers of Evil), first published in 1857.
The French auction website Osenat said the letter was bought by a private collector.
Baudelaire died at the age of 46, in 1867.