Is there anything wrong with leaving work early when you know that not much productive is going to happen in the last three-quarters of the hour or so?
Much of it depends on the industry in which you work, and the office culture at your work. It also depends on what you mean by "wrong" here.
If you mean in the legal sense, you need to become familiar with local laws. That's not something we can help with in this forum.
If you mean "is there anything wrong with choosing to ignore the corporate culture and norms", that's a more difficult discussion. Some individuals in a unique and safe position can deliberately ignore the norms and get away with it. Most cannot.
If you mean "Can I decide to leave early when my boss specifically tells me to work longer?", then you need to determine what kind of outcome is possible, and what kind of outcome you desire.
- If you cannot be fired no matter what you do, and if a potentially poor job review doesn't impact you, then it's not "wrong" to leave whenever you choose.
- If you can be fired but don't care, then it's not "wrong" to leave whenever you choose.
- If you can be fired and you do care, then you should talk with your boss, explain your limited attention span, and ask if there can be some accommodation
You indicate that "not much productive is going to happen in the last three-quarters of the hour", but that's something you can change. Being "spent" is a matter of opinion, not fact. Even if you are tired, there are productive things that you can accomplish - ask your boss to suggest tasks that can be successfully completed in a tired state.
is this what is expected at a "real/corporate" work place?
At least in my part of the world, there are very few professional, salaried positions where 35 hours per week (or even 39 hours per week) is the norm. And while many jobs have some flexibility regarding the starting and ending time of those hours, many professional positions expect a higher level of commitment.
In France, it may be different.