Credit belongs to the Islamic world for keeping classical knowledge alive and reintroducing it to Europe at the beginning of the Renaissance. However the Enlightenment refers to a later period in European history where people came to terms with the result of decades of very nasty civil wars over Protestant vs Catholic, and came up with principles which allowed people of different beliefs to peacefully coexist within society.
That is the source of Western ideas like "freedom of religion" and "freedom of speech". Which very importantly say that while you can take offense at another's words or beliefs, you can't actually do anything about it. Like go over and kill them. And they have to reciprocate by not killing you in turn.
The Muslim world has nothing like this. Sure, they say that you're free to follow another religion of the book. But their teachings are very explicit that this only works so long as you don't do anything offensive to muslims. Like mock the prophet, convert muslims to your faith, and so on. Do that, and you die. Unless the Muslim world internalizes the Western version of that idea, we're going to continue having problems reconciling Islam and Western civilization.
Incidentally the golden age of Islam that you refer to traditionally ended with the sack of Baghdad in 1258. However contemporary scholars point to evidence that relative enlightenment continued until the great economic decline that resulted from Western countries establishing direct trade routes with the East, which reduced commerce along the Silk Road.