Earlier quoted context omitted.
The only options I could think of that're mature enough are OCaml and Haskell. I'm aware of video transcoders in both, though nothing with anything like the format support of ffmpeg.
OCaml I know doesn't support SIMD acceleration. Not sure about Haskell. You need SIMD support to get anything decently fast in the field of video/audio manipulation.
There is also Intel Lab's HRC (Haskell Research Compiler) that does have SIMD capabilities [2]. Unfortunately, there isn't a public release of HRC yet.
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[1]: https://ghc.haskell.org/trac/ghc/wiki/SIMD
[2]: http://dorchard.wordpress.com/2013/10/14/automatic-simd-vect...