If you run Fiddler with your application that has the following code. You will notice that the not found exception was raised by this web request: http://webservices.cartosphere.com/arcgis/rest/services/FranceRaster/FRANCERASTER_V20_FRA_L93/MapSer...
<esri:Map>
<esri:ArcGISTiledMapServiceLayer Url="http://webservices.cartosphere.com/arcgis/rest/services/FranceRaster/FRANCERASTER_V20_FRA_L93/MapServer"/>
</esri:Map>
You need to set Token property. You can read this blog post: http://blogs.esri.com/Dev/blogs/silverlightwpf/archive/2010/02/15/How-to-use-secure-ArcGIS-Server-se.... If you know username, password, you can generate token from this link: http://webservices.cartosphere.com/arcgis/tokens