Your unedited question had a French sentence in it that I am not fully bilingualinterpret as:
Our software XYZ allows the resizing and conversion of PNG images.
Please note that the edit appears to have changed convert to modify, but I can generally understand written Frenchwhich have different meanings with respect to image files.
To answer the three questions posed above, though...
"Our software XYZ allows to resize and modify PNG images."
Does the latter sound strange for a native English speaker?
This does sound strange, yes. It could be reworded as I wrote above, or you could focus the images depending on the verb tense you desire:
Our software XYZ allows PNG images to be resized and modified.
Which one is more idiomatic? ("to allow somebody to do something" vs. "to allow to do something")
The second one does not strike me as grammatically correct, thisso the first one is more idiomatic by default.
Is there another way to say it without involving "the user" with another verb than "allow"?
You could use a number of synonyms that would retain the same basic structure of the sentence reads:
Our software XYZ allowspermits the resizing and conversion of PNG images.
Our software XYZ enables the resizing and conversion of PNG images.
Our software XYZ provides the ability to resize and convert PNG images.
One final note: I don't know the complete context in which this text would belong, but it feels to me like the "Our software" is redundant, and you could probably simply write:
XYZ can convert and resize PNG images.