I'm french, I think I can complete other answers.
It's called "présent à valeur de futur", it express future the same way a future would, for some sentences it would sound less "french" to use future.
In your examples :
Je déménage demain.
Je vais manger avec Nicolas ce soir.
Would actually sound weird in future :
Je déménagerai demain.
Je mangerai avec Nicolas ce soir.
For this case the present tense is perfectly suitable. Wikipedia gives you some details about the case where you must use the "future simple" http://fr.wikipedia.org/wiki/Futur_simple
I'm not 100 % sure of that, but to my humble opinion when some action is certain and fixed in the future, it's better to use the present, the future expresses rather a project (in the case of an action in the future).
Nous nous marierons dans un an.
Suggests that not date has been defined, the project is here, but the event is still unclear about the when.
Nous nous marions dans un an.
Suggests that I can ask where and when it's plan to occured.
The use of "aller", doesn't let such details be expressed.
Nous allons nous marier dans un an.
Don't hesitate to ask for confirmation, I'm french so the theory of French is not clear for me, but I know what is used or not.