Let's start with what file cut you were using, please...While I don't really have a use for an axe living in the city there is no point in owning a dull tool. A coworker and former lumberman taught me a trick today on how to sharpen an axe or other impact edge.
Hold a file handle end above the edge and angled so the cutting teeth are perpendicular to the edge. Slide the file along maintaining a proper edge angle, do not move the file up and down. I quickly tried this today with my very dull axe and fuck me if it didn't put a damn sharp edge on it real quick.
Perhaps this is common knowledge for people who use them all the time but it was new to me and rather effective.