In fact é, ai, and è are 3 différent sounds. But while é and è are firmly established, ai sound is somehow floating between these two. So depending on people, accents, and even words, this sound will sometimes ressemble an é and sometimes ressemble an è. It's not specific to j'ai, but to all words with the ai sound (lait, fait, français, mais, frais, etc...) especially when the last consonnant is muted. For instance in pair, the r is not muted and the word is clearly pronounced pèr, same for caisse= kèss, plaine=plèn, fraîche=frèch. In most cases when followed by a consonnant, it will sound as è. Edit : after answering to Phil, I notice these words also enter in this category of muted e following the ai sound, so for the same reason it is pronounced è. But for muted endings it is floating. For instance I would personally say : - j'ai fait ça = jé fé ça. - oui, je l'ai fait = oui, je l'è fè. It's really hard to explain it, just habits, on the other hand no one will complain about which sound you choose, so you're free :-)

I’m not a native French speaker, but I’m fairly certain the *official* pronunciation of “j’ai” is jé (i.e. with a closed /e/, not an open /ɛ/). This carries over to the future tense: “je mangerai” ends in the é sound — unlike the conditional, “je mangerais,” which ends in the è sound. Notice that the future tense endings are the same as those of the present tense of “avoir,” while the conditional endings are the same as those of the imperfect of “avoir.” That being said, most Parisians and other Metropolitan French speakers no longer bother to distinguish between /e/ and /ɛ/. (They usually use a closed é in open syllables, and an open è in closed syllables. Thus, “événement tends to be pronounced évènement.) On the other hand, I believe most Québec French speakers are very good at distinguishing the two sounds, so all hope is not yet lost for us francophiles.

Everyone pronounces differently! I personally pronounce it "jé". You can listen to different native speakers here - you will hear both "jé" and "jè": http://forvo.com/word/j%27ai/#fr

The "J" is pronounced like the "s" in "pleasure": [ʒ] The "ai" in "J'ai" is pronounced like the "e" in "bet": [ɛ] So: --j'ai [ʒɛ]