Python code to weave rows
English code reads better, since the Python standard library is English.  If you use Dutch, though, please do so consistently.  Don't mix file_input and invoer, or def weave(self, weef_rij).

It's hard to understand what the task to be performed is, and what this code does.  Docstrings and doctests would be a good idea.

It is awkward how you do parts of the parsing all over the place:


strip_file = file_input.strip() and strip_file.split('=') in the main code.  It's especially bad that this snippet is placed before the imports, and before the next line of code (geweefde_rijen = nieuwe_rijen(invoer)).
invoer[i].split() within nieuwe_rijen().
int(coordinaat1[0]), int(coordinaat1[2]) within nieuwe_coordinaten().


It would be better to get the parsing done all at once, into a list of pairs of integers.  Not only would the code be easier to understand, it would also let the program fail earlier if the input is invalid.

I think you have overdone the OOP here.  There is not much point in defining a Coordinaat class, which is basically just a tuple, or CoordinaatRij, which is basically just a list.  All you need for this job is a few functions.

Specifically, it would be useful to take advantage of itertools.izip_longest(), which is the core of what you are trying to do.  Then, to transform the result repeatedly for subsequent rows, use the reduce() function.

from itertools import chain, izip_longest

def coordinaatrijen_parsen(tekenreeks, rij_scheidingsteken='\n'):
    """
    Yield each row of coordinates as a list of (int, int).

    &gt;&gt;&gt; list(coordinaatrijen_parsen('1,2 3,4=  5,6 ', '='))
    [[(1, 2), (3, 4)], [(5, 6)]]
    """
    for rij in tekenreeks.split(rij_scheidingsteken):
        yield [
            tuple(int(c) for c in coord.split(','))
            for coord in rij.split()
        ]

def weven(*rijen):
    """
    Interleave elements from the parameters.

    &gt;&gt;&gt; weven('Geeogn', 'odmre')
    ['G', 'o', 'e', 'd', 'e', 'm', 'o', 'r', 'g', 'e', 'n']
    &gt;&gt;&gt; weven('Gee', 'odmorgen')
    ['G', 'o', 'e', 'd', 'e', 'm', 'o', 'r', 'g', 'e', 'n']
    &gt;&gt;&gt; weven('Gd', 'o', 'eemorgen')
    ['G', 'o', 'e', 'd', 'e', 'm', 'o', 'r', 'g', 'e', 'n']
    """
    return filter(None, chain(*izip_longest(*rijen)))

if __name__ == '__main__':
    with open(...) as f:
        rijen = coordinaatrijen_parsen(f.read(), '=')
    resultaat = [(x + 1, y) for x, y in reduce(weven, rijen, [])]
    for coord in resultaat:
        print '%d, %d' % coord