Your options are (realistically): Websharper - full web stack, transparent RPC. Hard to interop with native JS libraries like angular though.
Funscript - F# to JS compiler, more minimalist approach.
F# server side (REST api in Nancy/Fanciful/WebAPI) teamed with javascript front-end. Also well worth checking out Livescript, syntax is very similar to F# but dynamically typed.
See also: A relevant blog article I posted: http://thecodedecanter.wordpress.com/2013/06/22/hosting-webs...
My consultancy (just in case): http://www.perfectshuffle.co.uk
Always up for a chat if you have some ideas :) Shoot me an email through website above or PM me.