I don't see anything wrong with this sentence. I agree with mgarizona that "ways in which" could be used, but I see no problem with sticking with "ways". "Discourses" in this context makes sense to me because there are many factions in French politics and they do not all agree when it comes to immigration. Islam and immigration are closely linked together since many French immigrants come from Islamic countries, so I would assume the sentence is referring to differing opinions about the Islamic presence and mosque establishments of French immigrants. Maybe the article looks at the issue holistically, which would include different discourses (should immigrants be allowed citizenship, should there be regulation of mosque establishments, etc). Also, over time the public discourse could have changed so that when the issue is revisited there would be two separate discourses. If in fact the article only presents one public argument then "discourse" should be used.
I agree with those who suggested discourse in the singular. It is used like the word conversation. Both words are acceptable in the plural, but sound better in the singular when used in a broad context, when you are not referring to a certain list of speeches or discussions but rather to the sense of what people say in general.
The use of "ways" is correct. The sentence is referring to more than one way Islam operates. It is not speaking of that way in a general combined frame. It is speaking in an inclusive frame of both of them. Therefore it needs the plurality.