English little word :

I'll not tell anymore what I wrote in my French self description,
Hello all :)
I'm Tom.I'm French. I'm doing physic studies (sports??), but my real passion is music!
I would learn or encrease (exchanging differents points of view) my English to write my own songs.
My goal here is to learn English language so that I can use English like English people use to speak it on the street.
I want to stop doing my usual simple sentences and make my vocabulary grows.

A Little Word in English little word : {or "A Few Words in English}

I'll not tell say any_more than what I write in my French self description,
Hello all! :)
I'm Tom._I'm French. I'm doing studying physics, studies, but my real passion is the music!
I would like to learn or encrease enhance* ( changing with points of view) my English to write my own songs.
My goal is here is to travelling {or traverse?} all of the English language, like English people use to speak it in the streets.
I want to leave** my usual simple sentences and make my vocabulary grow.

*Increase also means "to add", but since you explained that it was about "growth" with changing your point of view, I think "enhance" is the more appropriate word.

**You could also say "I want to get beyond my usual simple sentences", or " I would like to progress beyond..."