What makes French colonies such an interesting case-study is that, technically, when the French abolished slavery in 1794, the path for French citizenship opened up for all colonial subjects. The reality was much more complicated. In 1802, just 3 years after the French Revolution, slavery was brutally reestablished. Nevertheless, once equal rights have been offered, the idea cannot be taken away, and colonial-citizens had formed alliances with metropole republicans under enlightenment systems of knowledge.

Laurent Dubois is one of the foremost authorities on this subject, and it's worth looking into some of his books for a more complete answer. His nuanced study on Guadeloupe is one of the best I have come across: "A Colony of Citizens: Revolution & Slave Emancipation in the French Caribbean, 1787-1804"

I cannot address your question in lenghty details, but I'd like to leave a note addressing a specific aspect that has affected French colonies and former French colonies, and still affect them to this day. The French Revolution lead to a series of law reforms which evolved into what is now known as the Napoleonic Civil Code, or French Civil Code. As a lasting effect, most of what were then French colonies have a civil code inherited from - or inspired by - the Napoleonic Code. As a result, the state of Louisiana is the only in the US of A to have its own civil code instead of relying on the Common Law tradition. The province of Quebec holds a similar situation (although Quebec, or Lower Canada, wasn't part of the French empire anymore when the Revolution took place), as other Canadian provinces also are Common Law based jurisdictions. Most French colonies in Africa and Asia would later unherit from this Révolution française's creature, making it the most widely used civil law model around the world today.

Going back to the direct effects the French Revolution had on French colonies and their peoples, French revolutionary ideals were often used as a pretext for local reforms and/or popular uprisings. A notable example is Faustin Soulouque's bizarre reign over Haiti, he tried his best to copy French institutions and planned of spreading the Revolution thoughout the neighbourhood. He ended up believing he was the Carribean Napoleon, and his project soon bankrupted, but he was one of the many faces of the French colonial territories to embrace the French Revolution's philosophical ideas.

EDIT: Clarifications and grammar.

I'd love to ask, how did Revolutionary France keep a hold of these colonies?

Certain French colonies, such as Haiti (then known as Saint- Domingue), soon began to revolt, spurred on by the Creole middle class, as those who were of mixed race, but middle class, began to desire full control over the island. The revolution actually gave rights of citizenship to those born of two free parents, but the law was ignored, leading to the more bloody revolution.

source: The movie "Égalité for All: Toussaint Louverture and the Haitian Revolution " by PBS