The f2py docs state that one can use the has_column_major_storage(<array>) function to test whether this is true of NumPy arrays. However, this command results in an AttributeError: after compiling the example array.f from https://numpy.org/devdocs/f2py/python-usage.html using the command
f2py -c -m arr array.f -DF2PY_REPORT_ON_ARRAY_COPY=1 (as the docs indicate), one gets:

>>> import numpy as np
>>> import arr
>>> a = arr.foo([[1, 2, 3], [4, 5, 6]])
>>> arr.has_column_major_storage(a)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: module 'arr' has no attribute 'has_column_major_storage'
>>> print(numpy.__version__, sys.version)
1.17.3 3.6.7 | packaged by conda-forge | (default, Jul  2 2019, 02:18:42) 
[GCC 7.3.0]
>>> 

My guess is that the docs are outdated and maybe there is a new method to do the same thing, but I couldn't find it.