How to UTF-8 encode a character/string
If you have a wide character string, you can encode it in UTF8 with the standard wcstombs() function. If you have it in some other encoding (e.g. Latin-1) you will have to decode it to a wide string first.
Edit: ... but wcstombs() depends on your locale settings, and it looks like you can't select a UTF8 locale on Windows. (You don't say what OS you're using.) WideCharToMultiByte() might be more useful on Windows, as you can specify the encoding in the call.
To understand what needs to be done, you have to first understand a bit of background. Different encodings use different values for the "same" character. Latin-1, for example, says "é" is a single byte with value E9 (hex), while UTF-8 says "é" is the two byte sequence C3 A9, and yet UTF-16 says that same character is the single double-byte value 00E9 – a single 16-bit value rather than two 8-bit values as in UTF-8. (Unicode, which isn't an encoding, actually uses the same codepoint value, U+E9, as Latin-1.)
To convert from one encoding to another, you must first take the encoded value, decode it to a value independent of the source encoding (i.e. Unicode codepoint), then re-encode it in the target encoding. If the target encoding doesn't support all of the source encoding's codepoints, then you'll either need to translate or otherwise handle this condition.
This re-encoding step requires knowing both the source and target encodings.
Your API function is not converting encodings; it appears to be URL-escaping an arbitrary byte string. The authors of the function apparently assume you will have already converted to UTF-8.
In order to convert to UTF-8, you must know what encoding your system is using and be able to map to Unicode codepoints. From there, the UTF-8 encoding is trivial.
Depending on your system, this may be as easy as converting the "native" character set (which has "é" as E9 for you, so probably Windows-1252, Latin-1, or something very similar) to wide characters (which is probably UTF-16 or UCS-2 if sizeof(wchar_t) is 2, or UTF-32 if sizeof(wchar_t) is 4) and then to UTF-8. Wcstombs, as Martin answers, may be able to handle the second part of this conversion, but this is system-dependent. However, I believe Latin-1 is a subset of Unicode, so conversion from this source encoding can skip the wide character step. Windows-1252 is close to Latin-1, but replaces some control characters with printable characters.