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I use python 2.7.6 on win32.
If I enter u'\u010d'.encode('utf-8') to console, I get '\xc4\x8d' as response. That's correct.
But it I use C API for the same, I get incorrect '\xc3\xa8' as response. 
I was testing it on this program:
#include <Python.h>
int main() {
Py_Initialize();
PyObject* dict = PyDict_New();
PyRun_String("u'\u010d'.encode('utf-8')", Py_single_input, dict, dict);
Py_DECREF(dict);
}

In the C language, \u must be escaped as "\\u".

Indeed: the \u010d is being interpreted by your *C compiler* as a multibyte character, and the individual bytes of that multibyte character end up in the string that you actually pass to Python. I suspect that the actual bytes you get depend on your locale. Here I get (signed) bytes -60 and -115. (See e.g. "translation phase 7" in C99 6.4.5.)
As Victor says, you need to escape the backslash in the C code.

> I suspect that the actual bytes you get depend on your locale.
And from the output you're seeing, I'd guess that Windows is using the CP1250 (Latin: Central European) codepage to make the translation on your machine: http://en.wikipedia.org/wiki/Windows-1250.