That's true! But that's why I'm even more surprised, because I created 2 different orders, at 2 different times on the same day. A big order and a very small order (one product that I forgot). The chances that both of those orders are part of the 0.1% of "very late" ones are very slim...

Well, if most people here use it without issue, I guess there was a specific issue somewhere... Do they maybe put the international shipping at the back of the queue because "Well, it's far, they won't expect it fast anyway"?

I can tell you this. The customer service is some of the best out there today. Whenever I had an issue with Prime, I would tell them and they would take a few dollars off my monthly payment. Also, and this is recent, I called them and asked to be reimbursed for the past 6 months of inactivity. I told them "I forgot to cancel my membership," and they reimbursed my money no questions asked. So although anecdotal, I'm very satisfied with their services and have no problem joining again or recommending.

I once had a package arrive wet and late relative to the day it shipped.  Those were obviously shipping issues but Amazon still gave me a $50 gift certificate and let me keep the product, which worked fine despite being soaked.

Plus, from what I just read on the internet, Amazon.com seems to have a much better user rating than Amazon France, at least at one tracking site, despite the OP's anecdotal evidence and belief that Amazon.com needs to learn from them.  

If you read the OP carefully, you will see that I wrote "If this is something usual". If it isn't, like everyone here seems to think, then good. I guess I'll wait to finally receive those orders, and I'll try again in the future to see if it was really just bad luck on those one.

But the chances of a technical error on 2 different orders are slim, so I'm still trying to understand what is happening.

Yeah, I agree on that. I had a couple of issues with the shipping company in France sometimes, and the always shipped a new product right away for free, and then dealt with the shipping company themselves.

That's why I sent a ticket to their customer service. But weird stuff, I wrote the ticket on Amazon.com, and it was sent to and treated by Amazon France, who basically answered me "what are you talking about?". I explained and they answered that they passed the issue back to the US, and now I'm waiting for an answer.

I don't like to give Amazon my money, but when I have used it, everything came on time or earlier without Prime.

Well, I got an answer from Amazon...

They said that there was a "technical error" on both orders, they fixed it and they put my orders on priority shipping. I'm being charged for the priority shipping, but they will refund me after I receive the packages.

The normal shipping is supposed to take 9-12 days, the priority shipping is supposed to take 3-4 days. So with that, the expected arrival date of my orders changed... By 1 day. It is now written on the orders details pages that they will arrive one day earlier. Still 3 weeks and 1 day after I passed my order. Even with the 3-4 days shipping. 40 dollars more for the priority shipping, and they plan for an arrival in 3 weeks and 1 day instead of 3 weeks and 2 days. Wow, thanks guys!

At least they will refund me the 40 dollars, to get maybe my orders one day earlier... I hope that won't be the only change...