For two well-known examples of this in English, it’s common to say/hear
“Me and my friend” or “Him and I” (both incorrect)
instead of
“My friend and I” and “He and I” (both correct).
Similarly, I'm wondering if there are any (and if so, what they would be) prime, well-known examples of non-grammatical French structures that, while "technically wrong,” are so commonly (mis)used by French people that they are considered by many, if not most, to be "basically correct"?