Fêtes, etc.
(I just started this page, and will add to it when I feel like it. Right now I just have part of the summer and fall covered.)
Fête de la musique (June 21)
For more than 20 years now, Paris has held an annual Fête de la musique on the night of the summer 
solstice, and it's a party that lasts until dawn. It doesn't matter what day of the week the solstice falls on, come June 21, we have music in the streets, and we have it all night long. Well, it's music alright, but don't expect to hear the aria from Madame Butterfly (although I have heard some Bizet, for example, and other high-brow stuff). Basically the music part is an all but completely concealed excuse for one hell of a party. See, what happens is that pretty much everyone in Paris, the surrounding suburbs, and almost every country in Europe descends into the streets of Paris to dance, drink, party, yell, eat, throw stuff, and set fire to things. The only thing missing is firecrackers, and 
they'll wait until July 14 for that (see below). The party is absolutely great, if not sometimes a tad excessive. If you do not like crowds, not only will you not enjoy yourself here, you will be anything from mildly annoyed to bone-chillingly terrified. I guarantee there are more people on the streets at this event than you have ever seen anywhere. Many of the musical events are sponsored by the city; most are not. Many of the musicians are talented; most are not (and there's no correlation between these things). There are stages set up at all 
the places you'd expect (Bastille, the marais, Latin Quarter, Montmartre, basically any place two or more streets come together, and I'm really not exaggerating very much at all), and often there will be performances within fewer than 100 feet of one another, since people will just plop down and start singing or playing a saxophone or whatnot. It doesn't matter if the music is great or downright pathetic; people will gather in numbers ranging from the several dozens to the many thousands (really). Folks will set up kegs of beer, barbecues, card tables full of baked goods and sell to passers-by. Passers-by will buy these things (mostly the beer). Some folks have long-standing neighborhood gatherings, mostly in the older neighborhoods, that are especially charming, particularly since people come from all 
over for a sort of homecoming. The general atmosphere ranges from pleasant and homey (see Café la Comète, above right) to scary and gulag-like (as in the picture from the marais above); the three pictures above were all taken within 2 hours of one another, just so you have some idea of how different the various neighborhoods can be. On one corner you'll have a metal band shrieking out lyrics calling for the death of all puppies; walk down the street and a golden-haired teenager will be singing plaintively about social injustice. Attending both events will be a near stunning, practically impossible mix of blue-haired old ladies and hard-core skinheads. You takes your pick.
[One of Tom's favorite anecdotes: A short while back, my friend Teresa, who occasionally rents an apartment to tourists, told me that she felt bad that she forgot to tell a tenant about the noise that the Fête de la Musique might cause. The woman told her that she had read all about it on a website called Tom's Guide to Paris. Teresa mentioned to her that she was having dinner with me that very evening, and the woman gasped: "You know Tom?!"]
Gay Pride
It's the same day everywhere (last Saturday in June), and it's huge in Paris. In 2014, according to official reports, there were more than 650,000 spectators and participants. Various commercial and civic enterprises are represented, including the Hôtel de Ville (Paris has an openly gay mayor), the RATP (metro), Air France, and the police. Expect the usual club music, dancing, and leaflets.
Quatorze Juillet
Celebrates the anniversary of the French Revolution (1789). Sort of like our 4th of July, but less nationalistic in some senses, more in others, and far more protracted in its celebratory effects. That is, you'll never see a French peson waving a flag—that is reserved for the big military stuff, of which there is sufficient amount to satisfy even the most hawkish fool—but the celebration lasts approximately 24 hours. The big things, as far as I'm concerned (and as far as you're concerned this is Absolute Truth) are the parties of the night of the 13th, and the fireworks on the 14th. There is also, as I mentioned, the big military parade. It takes place on the afternoon of the 14th, I think someplace around République, and it's pretty scary. The dancing and parties of the 13th, however, are charming and extremely fun, if you do it right. You should get a lot of sleep before going out, because you're most likely going to be out until dawn. There will literally be dancing in the streets (and beaucoup drinking, too), with live bands galore. One important thing to note: people will be throwing firecrackers—unfortunately, quite a lot—out of passing cars and whatnot. If you're afraid of firecrackers going off near you, you might find this evening somewhat trying. The best places to go on the 13th are: (1) the Hôtel de ville. Go here first, because although it's a big celebration, it's somewhat impersonal and doesn't have much character. (2) the Bal des pompiers (Firemen's Ball) on the rue de Sévigné, just across from the metro Saint-Paul. This is truly not to be missed. There are similar fireman's balls all across the city, but this is far and away the best one. Go here around 11:00 or midnight. You'll go through some big doors into a courtyard, and the firemen will have a big box and ask you for a donation. Throw in a few euros (they don't care how much, but you should give them something), and proceed through the courtyard into the much larger court to the back and to the right. There'll be a reasonably good band, usually playing traditional as well as contemporary music, a huge bar with cheap beer and wine, and dancing, dancing, dancing. This will go on to all hours, and the crowd here is extremely lively and friendly (but you will note that French people aren't the best dancers in the world). If it's not too crowded, you will have an absolutely marvelous time. Then, (3) at about 2:00 - 3:00 A.M., if you're still into it, there's an even bigger (and somewhat weirder) dance along the edges of the Seine run by the radio station Féquence Gai. It's mostly gays and lesbians, but no one cares if you're straight, as long as you're not some kind of homophobe; go and you'll have have an amazingly great time. It tends to be on the left bank just across from Notre Dame, so it's only about a ten-minute walk from the Firemen's Ball. This will go on until dawn, and there'll be weird contests—stripping, singing, etc.—as well as dancing to more contemporary music. Things will sort of quiet down a bit along about 5:00 A.M., and then you can sit down on the banks of the river and watch the sun 
come up. The morning light throws the river and this part of the city into a remarkable cast, and you have not seen Paris until you see it like this. Have breakfast afterward. The fireworks on the 14th are usually shot of from the Seine, and most folks congregate on one of the bridges toward the Eiffel Tower. Dancing continues on the night of the 14th, in slightly (but not much) subdued fashion. The best I've found is at the Place Contrescarpe, at the top of the rue Mouffetard. Go here and I promise you'll love it.
Fête des vendanges de Montmartre
Celebrated during the second weekend in October, this is when they harvest the grapes from the vines in Montmartre. Really. About a thousand years ago there were considerably more vinyards here; now there's just a little plot of land right by the Lapin Agile, at the corner of the Rue des Saules and the Rue Saint-Vincent. Apparently they're able to produce a few hundred bottles of wine per year from these vinyards, and it also seems that the wine pretty much sucks, but people are into this largely for the symbolic value: there are working vinyards right in Paris. There's a parade, refreshments, and all sorts of other activities going on here for the festival.