PDFBox U+00A0 is not available in this font's encoding

You'll have to embed a font and not use WinAnsiEncoding:

PDFont formFont = PDType0Font.load(doc, new FileInputStream("c:/windows/fonts/somefont.ttf"), false); // check that the font has what you need; ARIALUNI.TTF is good but huge
PDResources res = acroForm.getDefaultResources(); // could be null, if so, then create it with the setter
String fontName = res.add(formFont).getName();
String defaultAppearanceString = "/" + fontName + " 0 Tf 0 g"; // adjust to replace existing font name

Note that this code must be ran before calling setValue().

More about this in the CreateSimpleFormWithEmbeddedFont.java example from the source code download.