What you are hearing in French is the /j/ glide. You can hear it on forvo.com in the words travail /tʁa.vaj/, Versailles /vɛʁ.saj/, as well as many others. Listening to these pronunciations, I hear some French speakers pronouncing it so it sounds like it rhymes with tie, and others pronouncing it so it sounds like it has an extra "yeh" at the end. French speakers are probably not going to hear the difference between these two pronunciations unless they listen for it.
This /j/ glide is not an English phoneme that can occur at the end of a word.
Americans generally pronounce foreign words with English phonemes (this is the reason that we often pronounce Bach with a /k/ and Goethe with a /ɜr/). The English pronunciation /vɛrˈsaɪ/ is as close as you can come to the French pronunciation with English phonemes. You certainly don't want to pronounce Versailles so it rhymes with (say) messiah, as that would sound worse to both the French and Americans.