When writing stories in English, descriptive sentences often go like this: "action, description". Action is: "Eric fell asleep". Description is: "his head gently tipping to one side". A comma between the action and description is required. You're translation is correct, but very unpoetic (sorry :)). It sounds much better and more interesting to not use the "while" and "was" you added.

'Eric fell asleep, his head gently tipping to one side'? Eric has fallen asleep , and his head has dropped to one side ( from above sentence , we can assume that he was sitting when he fell asleep ,like in an aeroplane , and that the exact moment Eric fell asleep , his head slowly dropped to one side to tip > to move to a slanting position