Haiti was hit by a devastating earthquake in January this year that killed more than 250,000 people and left much of the country in ruins.
Campaigners, including Noam Chomsky, the US linguist, and Naomi Klein, the Canadian author, described the debt as "patently illegitimate ... and illegal".
"The 'independence debt', which is today valued at over 17bn euros illegitimately forced a people who had won their independence in a successful slave revolt, to pay again for the freedom," the letter, published in Britain's Guardian and France's Liberation on Sunday, said.
Haiti launched a lawsuit in 2004 to recover the money, but it was abandoned after France backed the overthrow of Haiti's government.
The letter said such actions were "inappropriate responses to a demand that is morally, economically, and legally unassailable".
"In light of the urgent financial need in the country in the wake of the devastating earthquake of January 12, 2010, we urge you to pay Haiti, the world's first black republic, the restitution it is due," it said.
Haiti, then St Dominique, was France's most profitable colony due to the slave trade.
In 1791 the slaves revolted, and in 1804, after defeating Napoleon's armies, the world's first black republic was founded.
France subsequently demanded the independence debt to compensate former colonists for the slaves who had won their freedom, and threatened a military invasion if the money was not paid.
Sunday's letter has also been signed by members of parliament from Europe, Canada and the Philippines, along with scholars, journalists and activists in France, Haiti, the US, Canada, the UK, Nigeria, Sierra Leone and Germany.