Can't seem to find their phone number. Do they accept reservations?

No reservations at Au Cheval. When you wall in, in person, you can put your name in the waitlist with your name/number and give you an ETA. Generally speaking, it can get pretty packed there, so keep that in mind with your day plans, if you want to venture out to check out the place

They do not.

No reservations. You walk in, they give you a time estimate and you give them your mobile number to save your spot. They call you when you can be seated with a 10 minute grace period.