IMO it's better to think of each particular programming language as a stage and your goal is to practice acting.
Learning multiple programming languages at once is more like trying to learn Spanish and Portuguese simultaneously. It's not impossible, but you'll find yourself doing "double duty" because your brain has yet to develop clear lines between the two languages.
I've directly taught hundreds of people how to code and have seen this first hand. Take a beginning programmer who knows a little Python (or Java or C or anything), teach them some basic Ruby syntax, and ask them to write a Ruby program, they'll write in a creole of Ruby/Python, Ruby/Java, Ruby/C, etc. (cf. http://en.wikipedia.org/wiki/Creole_language)
I'm not kidding. You'll see things like this from C or Java programmers
def Fixnum add(Fixnum x, Fixnum y)
return x + y
end
Untangling those false connections just adds overhead to the learning process and (IMO) are best avoided until you have a clearer mental distinction between programming _per se_ and programming in a specific language.
I've tried it before (with different technologies), and although it didn't make me an expert in either field, I've found it neatly ties most things together.
Oh, and it's usually fun, especially if you put somewhat bizarre obstacles in your way (remember, it's a learning experience, not production code). It could be something elaborate like http://www.xpteam.com/jeff/writings/objectcalisthenics.rtf or just a concious decision to implement a part of the design in a part of the system where it isn't most obviously at home.
This will help you develop a better sense of how F# and JavaScript differ as languages, what ideas are natural in one but unnatural in another, the conventions and idioms around tackling certain problems, and so on.