plaintext = input(\"Please enter the text you want to compress\")
filename = input(\"Please enter the desired filename\")
If you use Python3x then string is not the same type as for Python 2.x, you must cast it to bytes (encode it).
plaintext = input("Please enter the text you want to compress")
filename = input("Please enter the desired filename")
with gzip.open(filename + ".gz", "wb") as outfile:
outfile.write(bytes(plaintext, 'UTF-8'))
Also do not use variable names like string or file while those are names of module or function.
EDIT @Tom
Yes, non-ASCII text is also compressed/decompressed. I use Polish letters with UTF-8 encoding:
plaintext = 'Polish text: ąćęłńóśźżĄĆĘŁŃÓŚŹŻ'
filename = 'foo.gz'
with gzip.open(filename, 'wb') as outfile:
outfile.write(bytes(plaintext, 'UTF-8'))
with gzip.open(filename, 'r') as infile:
outfile_content = infile.read().decode('UTF-8')
print(outfile_content)