First of all, the standard interface for browser plugins is NPAPI (Netscape Plugin API). More recently, there's been a move towards Pepper. However, I would strongly discourage you from making a browser plugins. Users hate it and it's generally really suspicious since plugins let you do more or less anything with a user's computer.
If you're really set on using native code, your best bet is probably Google Native Client (NaCL). This lets you run native code at near native speeds within a sandboxed environment. It's already been used to port Bastion to the Chrome web store thingy. This also has the advantage over a normal plugin of being at least somewhat cross-platform. It requires a specialised compiler toolchain which (from memory) currently uses GCC/G++. Mono has also been ported to NaCL, so you can run C#, F#, Java (via IKVM), etc.
That said, it still requires your users to install a plugin if they aren't using a very recent version of Chrome, but at least they only need to trust Google as opposed to some random developer they've never heard of before.