str is text representation in bytes, unicode is text representation in characters.
You decode text from bytes to unicode and encode a unicode into bytes with some encoding.
That is:
>>> 'abc'.decode('utf-8') # str to unicode
u'abc'
>>> u'abc'.encode('utf-8') # unicode to str
'abc'
UPD Sep 2020: The answer was written when Python 2 was mostly used. In Python 3, str was renamed to bytes, and unicode was renamed to str.
>>> b'abc'.decode('utf-8') # bytes to str
'abc'
>>> 'abc'.encode('utf-8'). # str to bytes
b'abc'
You are using encode("utf-8") incorrectly. Python byte strings (str type) have an encoding, Unicode does not. You can convert a Unicode string to a Python byte string using uni.encode(encoding), and you can convert a byte string to a Unicode string using s.decode(encoding) (or equivalently, unicode(s, encoding)).
If fullFilePath and path are currently a str type, you should figure out how they are encoded. For example, if the current encoding is utf-8, you would use:
path = path.decode('utf-8')
fullFilePath = fullFilePath.decode('utf-8')
If this doesn't fix it, the actual issue may be that you are not using a Unicode string in your execute() call, try changing it to the following:
cur.execute(u"update docs set path = :fullFilePath where path = :path", locals())
As has already been pointed out in the comments, there is already advice on porting from 2 to 3.
Having recently had to port some of my own code from 2 to 3 and maintain compatibility for each for now, I wholeheartedly recommend using python-future, which provides a great tool to help update your code (futurize) as well as clear guidance for how to write cross-compatible code.
In your specific case, I would simply convert all calls to unicode to use str and then import str from builtins. Any IDE worth its salt these days will do that global search and replace in one operation.
Of course, that's the sort of thing futurize should catch too, if you just want to use automatic conversion (and to look for other potential issues in your code).
You can test whether there is such a function as unicode() in the version of Python that you're running. If not, you can create a unicode() alias for the str() function, which does in Python 3 what unicode() did in Python 2, as all strings are unicode in Python 3.
# Python 3 compatibility hack
try:
unicode('')
except NameError:
unicode = str
Note that a more complete port is probably a better idea; see the porting guide for details.