To decode characters properly, you need to understand how they are encoded. If all you have are the plain strings, then some ... guesswork ... can't be avoided. Also note that copypasting encoded UTF-8-strings doesn't work well: The UTF-8-encoding of àáâä contains bytes which are non-printable control characters. Here, on PerlMonks, these are converted to spaces, so I can't even work with your example string.
Your second test string does not look like doubly UTF-8 encoded: Try to find out how you created that string, and then we can work from that. If I doubly encode àáâä, I get:
Nitpick: your question would be easier to read with a little formatting. You can edit your post to add HTML for lists, and code (or examples) are better wrapped between <code> and </code> tags.