tl;dr Use a context manager.  See the bottom of this answer for important cautions about them.
Files got more complicated in Python 3.  While there are some methods that can be used on normal user classes, those methods don't work with built-in classes.  One way is to mix-in a desired class before instanciating it, but this requires knowing what the mix-in class should be first:
class MyFileType(???):
    def __init__(...)
        # stuff here
    def close(self):
        # more stuff here
Because there are so many types, and more could possibly be added in the future (unlikely, but possible), and we don't know for sure which will be returned until after the call to open, this method doesn't work.
Another method is to change both our custom type to have the returned file's ___bases__, and modifying the returned instance's __class__ attribute to our custom type:
class MyFileType:
    def close(self):
        # stuff here
some_file = open(path_to_file, '...') # ... = desired options
MyFileType.__bases__ = (some_file.__class__,) + MyFile.__bases__
but this yields
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: __bases__ assignment: '_io.TextIOWrapper' deallocator differs from 'object'
Yet another method that could work with pure user classes is to create the custom file type on the fly, directly from the returned instance's class, and then update the returned instance's class:
some_file = open(path_to_file, '...') # ... = desired options
class MyFile(some_file.__class__):
    def close(self):
        super().close()
        print("that's all, folks!")
some_file.__class__ = MyFile
but again:
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: __class__ assignment: only for heap types
So, it looks like the best method that will work at all in Python 3, and luckily will also work in Python 2 (useful if you want the same code base to work on both versions) is to have a custom context manager:
class Open(object):
    def __init__(self, *args, **kwds):
        # do custom stuff here
        self.args = args
        self.kwds = kwds
    def __enter__(self):
        # or do custom stuff here :)
        self.file_obj = open(*self.args, **self.kwds)
        # return actual file object so we don't have to worry
        # about proxying
        return self.file_obj
    def __exit__(self, *args):
        # and still more custom stuff here
        self.file_obj.close()
        # or here
and to use it:
with Open('some_file') as data:
    # custom stuff just happened
    for line in data:
        print(line)
# data is now closed, and more custom stuff
# just happened
An important point to keep in mind: any unhandled exception in __init__ or __enter__ will prevent __exit__ from running, so in those two locations you still need to use the try/except and/or try/finally idioms to make sure you don't leak resources.