Hi
For a person not being native with English not their first language I must say it's much better than many born speaking English
With that said personally I would contact them initially by phone, and strike up a conversation. Usually at some point during the conversation, I am asked whether I have a resume/CV and would care to submit it. This immediately gives me an indication as to whether they are interested in me. This is the way I have always approached employment with great success. It is definately well worth having your resume/cv ready and properly prepared as you will always be asked to submit It at some point, even if they show interested over the phone.
A good well written, concise resume/cv is a must and should be prepared and updated. The phone call makes you stand out from the many hundreds your prospective employer may have already on file.
Hope this helps