In German, this type of handwriting is normally called Sütterlin, although technically that only refers to a specific late simplified variant (due to Ludwig Sütterlin) that was last taught in schools. Another common way of referring to this, which is properly applicable to the older forms as well, is [alte] deutsche Schreibschrift. And finally there is the proper technical term deutsche Kurrentschrift, which is rarely used by the general public and probably not understood by everyone.
PS: Apparently I wasn't clear enough. "Deutsche Kurrentschrift" is the proper term and is used among experts. But it is practically unused among the general public to the point that many Germans don't know what it means and would guess that it refers to something else they haven't heard of. "Deutsche Schreibschrift" is also heard occasionally, but is ambiguous. "Alte deutsche Schreibschrift" is slightly less ambiguous but is used even less frequently due to its length. (It is still ambiguous because other forms of handwriting were popular in Germany even earlier.) "Sütterlin[schrift]" properly refers only to the latest variant, but most people don't know this and are not able to distinguish different forms of Kurrentschrift anyway.
By the way, there are two forms of Sütterlinschrift, only one of which is a Kurrentschrift. This makes it even more wrong to refer to all forms of Kurrentschrift as Sütterlin, but in linguistics and lexicography, ultimately the users of a language are always right.