My webpage has the charset set to UTF-8 and that doesn't fix it.

Did you actually encode your webpage using UTF-8?

When UTF-8 is expected, I would expect exactly that output if the one outputs U+00F1 as byte F1 instead of bytes C3 B1.

In a UTF-8 terminal:

$ perl -E'say "\N{U+00F1}";'
?          <--- Actually U+FFFD, what you posted

$ perl -MEncode -E'say encode("UTF-8", "\N{U+00F1}");'
ñ
[download]

If it was an lack of decoding on input as you suspect, one would get multiple gibberish characters rather than the coding error indicated by the character you posted.

$ perl -MEncode -E'say encode("UTF-8", "\xC3\xB1");'
ñ
[download]

It sounds to me like you are properly decoding the text on input while failing to encode it on output.