Fontspec package makes font weird compiling with XeLaTeX

Fontspec package makes font weird compiling with XeLaTeX

I'm new to LaTeX. I'm using the 'fontspec' package and compiling the
document with XeLaTeX (xetex), but when I use the package:
\usepackage{fontspec}
The font is all weird, not behaving like it should. When I don't use
fontspec, the font is ok, but I lose the UTF-8 encoding, which I need,
like this:
With fontspec (bad font, encoding ok):

Without fontspec (font ok, bad encoding):

Any help is most welcome, thanks!