ArcGIS provides a free (and paid) API:
https://developers.arcgis.com/rest/geocode/api-reference/geocoding-reverse-geocode.htm
It provides an address for a given location (lat/lon). It doesn't even require an API key, but they suggest you get a free one to avoid rate limits.
Here is an example API call, with a JSON response:
http://geocode.arcgis.com/arcgis/rest/services/World/GeocodeServer/reverseGeocode?location=4.366281%2C50.851994&langCode=fr&outSR=&forStorage=false&f=pjson
