"Faux eucalyptus" refers to fake or artificial eucalyptus, which is a type of tree. It means that the eucalyptus is not real, but made to look like it. Full definition
Dress up a simple tree with faux eucalyptus stems, glitter branches, frosted pinecones, and metallic ornaments for a pretty and rustic look. (lionandlantern.com)
Thanks to the grapevine wreath base and faux eucalyptus garland on top, the creator of this simple spring wreath touts it as the easiest she's ever made. (countryliving.com)
Once you have painted the box, filling it with a layer of faux eucalyptus and adding the white pumpkins takes a few minutes at most. (momalwaysfindsout.com)