You could try the AttributeEncoder with “Replace invalid characters”=Yes to transform the string to e.g. Latin-1 (or whatever you require), then compare the string before and after so see if any extended Unicode characters where replaced/removed.

Since FME uses a PERL implementation of RegEx, then could use StringSearcher with RegEx to find where there is a string that has a match to a non-ASCII character, and the character positions.

RegEx Pattern looking for is >^^:ascii:]]

Gives

Thank you @bwn this helps us see the special characters that have snuck into our data. 
@david_ Thank you for also taking the time to submit an idea.  Your idea works in conjunction with @bwn.

First use the StringSearcher to find a Match for the UNICODE characters.
Then use the Attribute Encoder to remove them.
Then use the StringSearcher (during development) to confirm the UNICODE characters are gone.

Thank you both :)