I think there might be nuance in the way US and France see the political scale, but I guarantee that he is not considered left here.

At best center, but since his last policies (cutting rent assistance, giving tax breaks to the rich), even the "center" image starts crumbling

Indeed - language has been co-opted. In the UK we see the same thing "moderate" "centrist" - these now mean big-business friendly policies, to the right of previous right wing governments.