France had lost most of its overseas empire at the time of Napoleon because Napoleon had wanted to pursue a much more concentrated effort on Europe. Napoleon had seen the French loses in the French and Indian War (7 years war for Non-American/Canadians) and how most of French Canada and to an extent Spanish Florida were surrendered to the British. This resulted in him selling off Louisiana at a bargain price to the USA, also the Haitian Revolution was the nail in the coffin showing that France really didn't have anything left of consequence in the Americas, freeing up his focus for fighting in Europe.

Spain (and also Portugal, but since you didn't ask about it I'll save it for another time) had most of its empire in the Americas crumble as a result of the Napoleonic Wars, more specifically the Iberian Campaign. As you recall the Spanish lost Florida to the British, however they won it back during the American Revolution in exchange for the Spanish handing over the Bahamas. After that and the secret deals with Louisiana (which resulted in it switching hands between France and Spain until the French decided to official sell it to the US) not much had changed. Then when the French invaded in 1808 the Spanish didn't have any power to effectively police their territories in the Americas. So numerous provincial regions began seeing this as the opportunity to declare independence like the US did. You can see this with a lot of independence wars having the same general time frame of beginning-end Mexican War of Independence: 1810-1821; Bolivian War of Independence: 1809-1825; Argentine War of Independence: 1809-1818; Peruvian War of Independence: 1811-1824. Most of these were led by either Simon Bolivar or Jose de San Martin who were very good leaders and the fact that the Spanish throne had a serious continuity crisis and this resulted in turmoil culminating in a 3 year civil war.

You are partly correct in the British Navy did indeed help catalyze the events that would lead up to their independence but the thing that allowed it to occur wholesale was that the long-term instability caused Napoleon removing the Spanish crown and legitimizing it leading to a series of crisis preventing them from policing such a huge area.

As for the territories lost well, it depends on where you start. If you consider the period of the American Revolution and how it basically doomed France to its own Revolution, then I would have to say New France & Haiti, if not then I would say just Louisiana. For Spain it was the totality of their continental empire in the Americas with the last part (Florida) being lost in the Seminole Wars against the US.

Nothing was returned to the French or Spanish after the restoration of their respective monarchies because the Concert of Europe (Russia, Prussia, Austria, the UK being the great powers), only the UK had vested interests in the Atlantic trade and was comfortable with the Spanish tariffs against their goods being gone for good with their colonies independence & the fact that the French lands went to them made it all the sweeter. This idea is part of the reason why the British wished to support the US's Monroe Doctrine. However the Spanish did try, and, fail to reign them back into line.

A more interesting story would be the fate of Brazil & Portugal though.

I would argue that the Napoleonic wars were a big factor into jump starting the trend for the independence wars in Latin America. Napoleon deposed the Spanish king, Ferdinand VII, and replaced him with his brother, Joseph. Not a lot of Spanish or Spanish colonists were happy about this, as this completely undermined the hegemony and legitimacy of the Spanish authority. Naturally, there were resistance movements by the royalists, clinging to their loyalty to Ferdidand. The Spanish congregated in Juntas, sort of like committees. Now, here is where things start to piss more people off. These Spanish juntas were represented mainly by solely Iberians, and only represented the creoles, the American-born Spanish, by default. Sounds kind of familiar doesn't it? The creoles claimed that they were just as loyal to the "true king" as the Iberians were, and wanted equality to Spain, not subservience. So they pretty much said "We'll make out own juntas with blackjack and hookers in our own country" invoking popular sovereignty.

See, the creoles and the peninsulares, Iberian-born Spanish, had had a rivalry for decades. The creoles were upset that the peninsulares kept getting all the higher offices whilst they were stuck with the leftover positions(though, to be honest, they still had a lot of power over the populace). Creoles saw this time without a Spanish king as a sort of opportunity to gain power. Mexico had Father Hidalgo, a creole priest, and Father Morelos, a mestizo priest, stirring up the seeds of independence under the banner of nativism. The government put these two down in succession, but it only took that movement to set everything into motion.

You could also argue that the Napoleonic Wars brought the ideals of liberalism to Spanish America. Napoleon thought of himself as a liberator, spreading the ideas of the French Revolution. Simon Bolivar was very well versed in Enlightenment thought as were many fighters of the independence. So by the 1830s, revolutions cropped up all over Spanish America, and Spain lost its colonies.

Kind of a quick and dirty. You can check out "Born in Blood & Fire" by John Chasteen.