False.
Été and étais are pronounced differently.
Été is pronounced été, or [ete] using the International Phonetic Alphabet.
Étais is pronounced étè, or [etɛ] using the International Phonetic Alphabet.
The sound made by é is said to be closed. The sound made by è is said to be open. Using the International Phonetic Alphabet, the closed é is represented as [e]. The open è is represented as [ɛ].
The closed [e] can be heard in words like mes, les, blé, allé, des, thé.
The open [ɛ] can be heard in words like messe, belle, laide, faite, mètre. If you can say the English words get, wet, web, pen and men, you already know how to pronounce the open [ɛ] — the underlined letter in those words is the open [ɛ].
The open [ɛ] can also come at the end of a word, as it does in étais. A few other examples of words that end in the open [ɛ] include était, avait, voulait, lait.
Both vowels in été are closed — é or [e] both times. In étais, the initial vowel is the closed é or [e], but the final vowel is the open è or [ɛ].
You probably have no trouble pronouncing the closed [e] at the end of a word, like in été, mes, thé or blé. What you might have a little trouble with at first is pronouncing the open [ɛ] at the end of a word, like in étais, avait, lait or voulait.
Meh.
Meh is an informal English word used (often online) to denote a person’s indifference towards something. Meh, I don’t care. It’s a good example word because it ends in the open [ɛ]. Say it aloud a few times: meh, meh, meh, meh. The sound made by eh at the end of meh is the same sound made by ais at the end of étais.
With this knowledge, say été and étais aloud. Do you now hear a distinct difference between the two?
The ais, ait, aient endings of the imperfect tense (imparfait) are pronounced using the open [ɛ]. For example, allait (as in il allait) sounds like alè or [alɛ], whereas the past participle allé (as in il est allé) sounds like alé or [ale].
The imperfect endings ais, ait, aient may be pronounced so open, in fact, that they sound like a — like the a in ma, ta, sa or [a] using the International Phonetic Alphabet. This means, for example, that you could hear savait (as in il savait) pronounced like sava. You don’t need to pronounce the imperfect endings ais, ait, aient as [a] yourself, but you should indeed do your best to use [ɛ].
Compare:
été [ete]
étais [etɛ]
allé [ale]
allait [alɛ]
les [le]
lait [lɛ]