What kind of palm leaves or other material can be used for palm weaving?
Various kinds of material can be used for this, including palm, banana, and coconut leaves. In Zanzibar specifically, according to the website Zanzibar Tribal Art, grass and ilala palm are used in their weaving:


  The products of grass and ilala palm weaving (such things as sleeping mats) and basketry are associated with the widest possible range of activities throughout a Zulu’s lifetime, touching virtually every domestic, social, and religious function.  These baskets are evidence of the expertise of these artisans and their ingenuity for using indigenous plants.  Traditionally Zulu women weave the African Zulu baskets using age-old, time-honored methods that are passed on from mother to child.  The patterns, each with their own meaning, vary from decorative bands to intricate triangles, diamonds, zig-zags, and checkerboard motifs.


I don't know how easy such materials would be to find in Central Europe, but apparently it's a strong tradition in Italy, where:


  All over Italy you will find decorative palms that have been exchanged as gifts, hung above doors or been placed in homes for good fortune. The art of palm weaving itself involves twisting the palm leaves into elaborate decorative designs.


More generally, it's a Catholic custom, and done in Catholic communities of various countries including Germany and Poland. According to this blogger (emphasis mine):


  Keeping braided palms around the house is part of this Catholic culture, and I continue to practice it just as my parents and grandparents did. When I was younger, I tended to associate this tradition with yet another oddly rural thing my family still observed, but in reality it is not so much rural as it is a German and Polish Catholic tradition, which makes sense why my family did it. Sadly, it is starting to become a lost art. That is the thing with traditions; they are only continued if they are passed down to the next generation.


So it looks as though palm leaves suitable for weaving should be reasonably easy to acquire in various European countries.