TypeError: 'str' does not support the buffer interface

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)

There is an easier solution to this problem.

You just need to add a t to the mode so it becomes wt. This causes Python to open the file as a text file and not binary. Then everything will just work.

The complete program becomes this:

plaintext = input("Please enter the text you want to compress")
filename = input("Please enter the desired filename")
with gzip.open(filename + ".gz", "wt") as outfile:
    outfile.write(plaintext)

You can not serialize a Python 3 'string' to bytes without explict conversion to some encoding.

outfile.write(plaintext.encode('utf-8'))

is possibly what you want. Also this works for both python 2.x and 3.x.

For Python 3.x you can convert your text to raw bytes through:

bytes("my data", "encoding")

For example:

bytes("attack at dawn", "utf-8")

The object returned will work with outfile.write.