I'm a beautiful girl, I like music, and am interested in French and English. I think learning English will help me communicate better with a friend from another country.

That's a much better structed sentence. :)

First notebook entry: Introducing myself

I'm a beauty gir，i like music.and interested in Franceand English.I think learn English will help me exchange with some other country friend，so i want to learn English

Correction:

I am a beautiful girl.  I like music and I am interested in french language and english language.  I believe that learning english will help me communicate with people from other countries.  So, I want to learn english.

First notebook entry: Introducing myself

I'm a beauty gir what do you mean here? Maybe you mean..."I'm a beautiful girl?"，i I (I is always written as a capital letter when you are using it to refer to yourself...well, not that you use I to refer to another person...hehe sorry about that.) like music. , and I'm interested in France French and English. (put a space in between your period and the next sentence.) I think learning English will help me exchange (exchange what?) with a new foreign friend some other country friend，. so So, i I want to learn English