I cannot seem to figure out how to make an upper-case, cursive letter Z, like the one on the left in this picture. By using a french cursive environment, I can get the lower-case z, but the upper-case Z is not what I am looking for. Anyone know how to get LaTeX to make this font/symbol?
You can find a number of font alternatives that get pretty close to your sample at the LaTeX Font Catalogue, Calligraphical and Handwritten Fonts. Here are some options (although some are of questionable typographically technical quality, i.e. not vectorized fonts that look pixel-y):
Lukas Svatba has even more options. For information on how to implement a particular font, see the respective page in the Font Catalogue.