I published a routing service to my server with the network analysis capability. In the rest url I can see that for the Route layers the directions language is en for english and the directions supported languages is set to en, fr. How do I change the directions language from en to fr so my directions are in French?
Have you tried to set the streetDirectionsProperties language property? I believe you can do that from Python.
This doco page here is explaining the different properties for "streetDirectionProperties", and it has sample code as well: https://pro.arcgis.com/en/pro-app/latest/arcpy/network-analyst/streetdirectionproperties.htm
Are you publishing map service with network analysis capability from ArcGIS Pro or from ArcMap? If you publish from ArcGIS Pro, the service has the capability to return localized directions directly. You just need to pass "fr" to directionsLanguage parameter and you should get back directions in French.
If you publish from ArcMap, then you need additional resource files for the language you want to use on the server.
Let me know if you have other questions.