3 months

Today marks it's been 2 months that I'm far have been away from my home and my family.
I dwell live in France, in the French Alps. I moved to French Guiana and for my job I moved to french guiana for on a mission that would be normally last 3 months.
I'm in a place where there is no entertainment [no extra "e" and no comma here] during my free times.
Hopefully, my set time off will take place during the soccer World Cup, which should help me to have fun for a fit change (or "a while"). [I don't know what you meant to say here. I'm guessing.]
I hope the last month will pass quickly, at least I whish ["wish" is the correct spelling], because I miss my girlfriend and my dog.

Julien, here is what I think you want to say:

Today marks two months that I have been away from my home and family. I live in France, in the French Alps. I moved to French Guiana for my job on a mission that would normally last 3 months.
I'm in a place where there is no entertainement during my free time. Hopefully, my time off will take place during the soccer World Cup, which should provide some fun for a change. I hope the last month of my tour [or mission, or assignment] will pass quickly, because I miss my girlfriend and my dog.

Good job! One thing to note: The word "hopefully" is not supposed to be used the way you used it here, but almost everyone in America uses the word that way. It should be used as an adverb, as in this sentence: "My dog looked hopefully at the hamburger I was about to eat."

Keep up the good work, and I hope you can enjoy the rest of your time in French Guiana.

3 Months

Today it's been 2 months since I have been I'm far away from my home and my family.
I dwell live in France, in the French Alps and I had to relocate for my job I moved to French Guiana for a mission work project that will would be normaly last for  3 months.
I m in a place where there is no entertainement, during my free times. (Or where there is nothing to do in my spare time.)
Hopefully, my set off time off will take place be during the soccer world cup, which will entertain me for a while. help to have fun for a fit.
The last month would will hopefully pass quickly, at least I whish because I miss my girlfriend and my dog.