why does spoken french sound so fast?
because much of what separates french words on the page is gone by the time they are spoken. french carries the last sound of one word onto the first of the next, drops some of its vowels, lets a small word fall out of its negatives, and stresses only the end of each group of words rather than each word. a sentence reaches you as a few long, even stretches instead of a row of separate words. french is also quicker than english when you count syllables, though not when you count meaning. both are real, and the first is the part you can learn to hear.

more syllables, about the same message
in 2011 françois pellegrino, christophe coupé and egidio marsico recorded fifty-nine speakers of seven languages reading the same short texts, translated from english, at a normal pace. the french speakers averaged about 7.2 syllables a second. the english speakers averaged about 6.2. spanish and japanese were faster still, at about 7.8.
the same study measured how much each syllable carries. a french syllable carried less information than an english one, so the faster rate mostly made up the difference: for five of the seven languages, french among them, the information conveyed per second showed no significant difference. french is faster in syllables and roughly level in meaning. these were texts read aloud rather than conversation, and the authors note how much speakers and texts varied, but the shape of the result is clear enough. some of the speed you hear is the language's normal way of packing a sentence.
where the gaps go
the larger effect is the joins. when a word ends in a consonant that is pronounced and the next word begins with a vowel, french moves the consonant across, so it starts the next syllable instead of ending the last. linguists call this enchaînement. in a line from driftspeak's french volume built around before sunrise, cette place est libre ? ("is this seat free?"), the s sound at the end of place becomes the start of est. what you hear is closer to one word than two.
liaison goes a step further. many french words end in a consonant that is written but not said, until the next word begins with a vowel. then the consonant appears, and it too moves across. in ils ont l'air si heureux ("they look so happy"), from driftspeak's françoise hardy volume, the s of ils, silent on its own, is sounded before ont, and it sounds like a z. some of these liaisons are required, some optional, some forbidden, which is why they are hard to predict by ear. a word you know can arrive wearing a consonant that is not its own.
the vowels that fall away
some of the vanishing is written down. before a vowel, je becomes j', as in j'étais bien toute seule ("i was happy on my own"), another line from the hardy volume. that is elision, and it is on the page.
much of it is not. the unstressed e in short words like je, de and le is unstable in french: under certain conditions it is simply not pronounced, even before a consonant. one of the songs on françoise hardy's first record has the spoken form in its title, j'suis d'accord, "i agree". when it goes, it takes a whole syllable out of a sentence that a learner has been counting on.
the ne that goes missing
written french makes a verb negative with two words, ne before it and pas after it. spoken french often drops the ne. the linguist william ashby called it "a syntactic change in progress" in the title of a 1981 paper, and a later study of radio speech found the ne in decline across about forty years.
the hardy volume has both kinds of line. je sais pas comment ça va finir ("i don't know how it's going to end.") has no ne. ne me laisse pas ("don't leave me.") keeps it. a listener who waits for the ne to know a sentence is negative will miss the first one. in speech, the negative is often carried by the pas alone, after the verb.
stress at the end of the group
english gives most words a stressed syllable of their own, so an english listener is used to a beat in almost every word. french stress falls on the last full syllable of a group of words, a phrase or a short sentence, and word stress cannot tell two words apart. so the beats that would mark each word are missing, and the only strong syllable comes at the end of the group. to an ear expecting a beat per word, that sounds like a run.
how to hear the joins
listen for groups, not words. take one short line you have the text for, play it several times, and mark where the sound crosses the gaps on the page: the consonant that moved, the vowel that went, the ne that is not there. then say the line aloud the way you heard it, not the way it is written. the common short groups of french, the ones that open sentences or end them, are worth learning as single sound shapes rather than as strings of words.
this works up to a point. knowing the rules tells you what to listen for. it does not let you hear it at speed, which comes with hearing the same kinds of line many times.
one night of talking, a line at a time
driftspeak is subtitles for your ears. vol. 21 is built around richard linklater's before sunrise, fourteen tracks of short french sentences from the world of its one night of talking: a seat on a train, an invitation to get off, whether to say tu. each sentence is said in french and then in english.
cette place est libre ? ("is this seat free?") is asked across the aisle of a train in the first track of vol. 21; listen to a sample of that track, one of three with free samples, and hear it in french and then in english, then inside a longer question, and listen for the moment place runs into est.