How can there be a communist revolution in France instead of the French Revolution,
You can't: Communism didn't exist before Karl Marx wrote his manifesto and, as pointed out, he was born three years after the Restauration happened.
You could probably get a proto-Communist or ALT Communist ideology taking over if Gracchus Babeuf's ideas somehow became a majority during the time period. But Babeufism wouldn't necessarilly look like OTL Communism for one and the second thing is that getting Babeuf's philosphy to become the dominant one would be quite tricky... Babeuf only became a big figure by the time of the Directoire and even then he never really had a chance of toppling that regime... Hell, he was executed in 1797.
How would this affect Europe and the French colonial empire?
Not much considering that the French Revolution had basically turned all of Europe against it. Of course, assuming the French armies of this potential ATL Communist Revolution were as victorious as their OTL non-Communist counterpart, this could theorically have an impact on politics... But an impact that would come later on.
As for the colonies... Well, in 1789 the French colonial empire was basically reduced to Sugar Islands in the Carribeans... And a good deal of these sugar islands were occupied by the British during the Revolution. The non-occupied ones for their part benefited from a bit of autonomy thanks to the chaotic situation in Europe. So it's likely the revolution would have a limited impact on these islands, or at least I don't think it would be that different from OTL.
The case of Louisiana could also be discussed but I don't know enough it to tell you how the situation was going. Plus OTL, Napoleon ended up selling Louisiana to the US when he realised he could no longer build his American empire after Saint Domingue rebelled and became Haïti.
The relationship with the United States and the British Empire?
Considering the British OTL led or were behind most of the Coalitions against Revolutionnary and Napoleonic France... Well, I doubt there attitude would be that much different if France turned Communist.
As for the US, it depends on how good the relationship would be with this supposedly ATL Commie France. The case of Louisiana could prove problematic though as I've heard several people discuss the very real possibility to the US invading Louisiana if Napoleon hadn't sold it to them in 1803.
Independence of Spanish America and Brazil?
I doubt this would have an impact that much different from OTL. Though I guess the potential butterflies surrounding Napoleon could have an impact. After all, Napoleon's invasion of the Iberian Peninsula had big impacts in Latin America. In Spanish America, it created an instability that eventually led to the rise of Bolivar and other independantists. As for Brazil, the exile of the Portuguese royal family there is the reason Peter I fell in love with the country and created the Brazilian Empire as a monarchy independant from Portugal.
Would we have a Communist Napoleon?
Depends on when this ATL Communist revolution would take place... That being said, I have a hard time Napoleon embracing communism. He was a jacobin in 1793-94 sure but I'm not sure he was as radical as the leadership was at the time. Plus he eventually moderated his views quite a lot later on: the First Empire was basically a result of an attempt to recouncile revolutionnary ideals with more monarchic and conservative ones.
Again, it would depend on when Communism would take place but I seriously have my doubts about Napoleon becoming a communist. Plus it sounds a bit too much like saying Napoleon was the first coming of Hitler... Which is a historical nonsense: Napoleon's rule was authoritarian but he never reach the degree we would see in Totalitarian Dictatorships.
It is far too soon because communism needs industrialization to create the social/cultural prerequisites for communism andto give communist power its to old of mass control.
While I agree it's too soon to have a communsit revolution, I disagree about the need for industrialisation. Russia was still pretty rural when the 1917 Revolution happenned after all.
And I think It is impossible in France because the french are individualistic grouch. Here is a saying you may not know : "a frenchman is an italian in a bad mood."
Communism could probably not happen in France and if It ever happened on a local part of the french territory It would not last long because the french would quickly revolt.
Grouchy? ... Yeah, I guess we Frenchmen are a bit of a grouchy people that's always complaining...
That said, we don't always revolt. Or at least, most of the revolts we saw were generally more akin to the strikes we're so know for today: opposition to a new tax or a new law. When you look at history, we've had very few revolts that led to a change of regime in France. Last but not least, France has alwyas been a bit big on Centralisation and this centralised state has generally proven very effective at suppressing revolts.
Not saying you wouldn't see an opposition to the rise of a Communsit France (you had a Royalist/Counter-Revolutionnary opposition in 1789) but I'm just saying it wouldn't necessarilly led to a massive rebellion.