miTLS is a stack written in annotated F# and definitely a promising step in that direction https://github.com/mitls Unfortunately it doesn't offer a C-compatible ABI as far as I know, so not usable by native code applications.
http://caml.inria.fr/pub/docs/manual-ocaml/intfc.html
I'm not sure at a glance how easy it will be to use F star programs in C applications via Ocaml. We'd be better off if there was a compiler from F star to annotated/safe C, Ada/SPARK, or Rust. All of these can integrate more easily into the legacy apps.