perhaps you're missing something
that is, extra hour stuff aside

ONE day plus FOUR days is FIVE days, and a FIVE day rental is the same as a WEEK rental, therefore, an extra day on the four is a week.

After they changed it to a week rental, it reverts to the CURRENT WEEKLY rate. therefore, you got charged a higher rate (say, 400eur++)

I have seen people return a "weekend" rate rental late, and even though the rate was $15 each day for 2 days, the third day (extra hour or two over) was a full rate at $60 a day or something, causing a triple in the rental charges.

Edit--addition: If you were charged an extra day rate than listed on your contract, then you should be able to enforce it, but I would suggest that be done at the returning location before leaving, since it is usually easier in person.

Final note/disclaimer, since this is looks like it is getting heated--I am no longer connected with HTZ and have no sympathy for them. In fact, I pretty much hate the company (and previous parent F). I am only explaining how and why your charges could be so high.