One huge influence, though indirect, was Haiti. The French Revolution in Europe helped spark instability in the French Caribbean colony of Saint Domingue. What started as a conflict between the elites of the island escalated into a full on slave rebellion, culminating in Haitian independence by 1804. I would really recommend reading up on it, such as through classics like The Black Jacobins by C.L.R. James (multiple editions).

Events in Haiti are important for several reasons.

1. French planter immigrants fled to both mainland America and the Spanish Caribbean, including Cuba. These exiles built up new plantations there, bringing with them expertise as sugar and coffee plantation owners. They would eventually be almost entirely expelled from Spanish America when in 1808 Napoleon's forces invaded Spain. The phenomenon is given a rather summary treatment in Olga Portuondo's Cuba. Constitucion y Liberalismo, 1808-1841 (published by Editorial Oriente, in Santiago de Cuba, in 2008). I am aware of some very specialized literature existing on the subject, which to my knowledge isn't that well studied beyond what Portuondo puts forward, but it is mostly in very rare Cuban academic publications which cannot be accessed from the US. The phenomenon isn't really something that most histories of Cuba dwell too much on.

2. The example of the Haitian Revolution served to instill fear in whites, both in the USA, Cuba, and elsewhere, that political-military instability could bring on a slave uprising. The the slave regime in pre-Revolutionary Haiti was brutal, but so were the reprisals against whites as the ex-slaves emancipated themselves (even when accounting for exaggeration). The idea of 'another Haiti' would serve to scare whites and inspire free and enslaved blacks in the Caribbean for years to come. Manuel Barcia talks about this somewhat in The Great Slave Revolt of 1825: Cuba and the Fight for Freedom in Matanzas (Louisiana State University Press, 2013) but it is dealt with in more detail by Matt Childs in his book The 1812 Aponte Rebellion in Cuba and the Struggle against Atlantic Slavery (UNC Press, 2007).

Now, speaking of the French Revolution more generally, it had an undeniable influence in the Americas and Spain as well. There was even a term for those who had been influenced by French political and cultural ideas afrencesados (Frenchifieds). Admittedly someone influenced by French ideas could be attracted to more conservative ideas, like Voltaire's, than the Jacobins.

An interesting thesis, which I came across recently and have yet to accept completely, is Immanuel Wallerstein's proposal that the French Revolution should be seen as a cultural Revolution for those countries most connected to contemporary Capitalism since the impact of its ideas were so far reaching. (The Modern World-System IV: Centrist Liberalism Triumphant, 1789-1914, University of California Press 2011.)

As I specialize in Cuba I'm less able to help in terms of its impact on continental Hispanic America and the impact of French political ideas on Cuba seems to be fairly limited. Cubans tended to look to Great Britain (among more conservative elites) or the US (among those more liberal leaning) for their political paradigms, while they looked to France mostly as a cultural paradigm (music, literature, painting, etc).

Hope it helps!

I only saw this question now, but thought you might be interested in this earlier thread dealing with international influences on the Spanish American wars of independence more generally. This part from my answer deals with French influences, esp. on Bolívar:

French revolution/ Enlightenment: The French revolution's influence is evident in the French constitution's use (in translation) in most of the early Latin American state formations. A remarcable point was its assertion of the rights of man as self-evident, meaning that no royal or divine authority could take them away. Then again, in Spanish America citizenship remained narrowly defined and greatly circumscribed for decades, going back to Spanish and creole traditions. A more direct (non-revolutionary) French influence on Bolívar can be seen in his visit of Paris in 1804. He described seeing Napoleon's crowning himself as the culmination of the falsification of the French Revolution's principles. Despite his republican leanings, Bolívar would come to espouse more monarchical views towards his life's end.

The Enlightenments' 'pulse' could be felt in the new public sphere (including salons, newspapers, courts) not only in Europe, but also in Latin America. Except for its focus on rationalism and the respect for man, the Enlightenment did not produce a general political agreement: Individual features included support for limited monarchy, enlightened despotism, republicanism, representation government, or the protection of individual rights. Similarly, the Bourbon Reforms did not lead to a uniform political reaction. The need for an economical policy of their own (combined with the disadvantages suffered from free trade) motivated many Spanish Americans to move towards independence. In this way, the Bourbon Reforms deepened rather than weakened local autonomy that existed.

So regarding the Sp. American independence movement: The influence of Haiti has already been mentioned, but French intellectuals' writings and the French constitution were also very much absorbed by Latin American revolutionaries. We can add both the North American example and local Spanish American precedents and adaptations to these French influences - making it more difficult to determine specifically the impact of the French Revolution in this area. Nonetheless, its ideals including man's self-evident rights can be traced from earlier (like Hidalgo in Mexico) to later (incl. Bolívar) revolutionaries.