I was puzzled by the use of "puis" rather than "peux" in this example. I found this on Wiktionary.org: Puis (/pɥi/) is an archaic form of the first person present indicative peux. It is still used in inversion or with the conjunction si:<pre>
Puis-je vous aider? ― May I help you? Si je puis me permettre… ― If you don't mind…</pre>
Formal: Puis-je savoir pourquoi? Informal: Je peux savoir pourquoi? Formal: May I know why? Informal: Can I know why?
I'm not entirely convinced. I just put it out there.
For just a minute, you had me, it would be such a nice solution ... but then ... an objection: I could never formally ask anything that wasn't a question of permission. I could never say, for instance "Puis-je faire une difference?"
It's grammatically different. "puis-je" (the inversion for "je peux")/ "may I" is in present tense. "Could I" is in conditional.
I'm unclear what the distinction is. "May I" and "can I" are somewhat interchangeable in English, even if "may I" is technically more correct when asking a question.
There is a distinction in English between can and may although, you are right , it is not widely maintained nowadays. Technically, "can" implies ability to do something and "may" implies permission.
"Stop, Smith minor! I'm sure you can hit Jones major at 20 yards with your catapult - but you may not. Please get on with your work".
We would not normally say 'Can I know. why?' In English. We would say 'May I know why?' or 'would you tell me why?' But we just don't use the expression 'Can I ' in a sentence like this.