Answer

Hello A.,
In short: it seems that the mezuzah should not be placed the way you put it. It should be changed to an upright position for Sephardim, or to a diagonal position with the top leaning inward for Ashkenazim. I suggest you take it down and reattach it without a blessing.
There is a dispute in the Talmud and among the medieval authorities (Rishonim) whether the mezuzah should be placed upright or lying horizontally inward. From the wording of the Talmud it appears that if it was done improperly, it is invalid—there is only a disagreement over what counts as proper. Therefore, Sephardim place it upright, while Ashkenazim adopted the custom of placing it diagonally in order to accommodate both views.
It follows that a reverse diagonal like the one you used is indeed considered upright because of its vertical component, just like the accepted diagonal placement, but you lose the horizontal dimension because it is reversed. Therefore, it seems that according to Sephardic practice, what you did may be acceptable after the fact, since there is still a vertical component, and from Ashkenazic custom we see that a vertical component counts as upright. But according to Ashkenazic practice, you have entirely lost the horizontal dimension, and seemingly it is invalid.
So it seems to me that for Ashkenazim it definitely should be reattached, and for Sephardim it may possibly be left as is after the fact, although in my opinion it is still proper to be stringent and reattach it. In any case, because of the possibility that you may already have fulfilled your obligation beforehand, you should not recite a blessing when reattaching it.
All the best,