First off, that’s a French name, not English. (Avenue des Champs-Élysées is the name of the major thoroughfare in Paris.) Secondly, the proper spelling requires those ‘é’ characters. Those accents cannot be cavalierly disregarded: The character ‘é’ is not the same as an ‘e’ character. The French are sticklers about this, even if they habitually leave off the accents when spelling words in all capital letters.

Now, listen to a French speaker pronounce “les Champs-Élysées”.

That would be enough for someone who already spoke French, but English speakers tend not to hear everything that a native French speaker will swear is being enunciated. While you may hear something like “shon-zayly-ZAY”, if you say that to a French speaker they will say, “That’s close, but not quite right.” They think they are pronouncing the ‘m’, ‘p’ and ‘s’ in “Champs”, even though those who don’t speak French don’t hear anything but the ‘s’, and that’s more like a prefix to the next word (“zayly-ZAY”). They also don’t think that they’re saying anything that sounds like ’n’ for the ‘mp’ character sequence. This kind of thing drives non-French speakers trying to say French words nuts. The French think that foreigners are just stupid.

What’s going on here is made a little clearer when you look at the IPA rendering, “ʃɑ̃z‿e.li.ze”. You’ll notice that the single character ‘ã’ represents the three-character sequence ‘amp’. For those who know Portuguese, you’ll recognize this character from place names like “São Paulo”. This phoneme is a nasal honking sound composed of a subtle, rapid transition between two sounds, something like “ah” and “uhn”. The ’n’ is almost not there at all, but English speakers tend to hear it as the ‘ã’ sound closes off. Whatever you do, don’t bear down in pronouncing that ‘n’.

You learn something else if you watch carefully as a native French speaker says this phrase. They really are shaping their mouths, that is, briefly closing their lips, for the ‘m’ and ‘p’ consonants even if no sound can be detected. If you do this, it puts a slight pause between “shã” and “zayly-ZAY”. This little pause helps to get closer to the authentic way of saying the phrase. It may upgrade you from “close” to “pretty good”.

One more thing needs to be said. The standard way of pronouncing “Champs-Élysées” is shortened and clipped in the same way that people in other countries pare down familiar place names. The English say “Gloster” for “Gloucester” and “Woostersher” for “Worcestershire”. Some Americans say “Wash’ton” for “Washington” and some don’t. “New Orleans” may end up as “NOO-or-LEENZ”, “noo-OR-linz” or even “NAW-linz” depending on where you’re from. None of these is pronounced anything like “Nouvelle-Orléans”, which is what the French call the city in their former colony, named after their own city of Orléans ​[pronounced ɔʁleɑ̃].