In regards to the Perl code, why do you do eval('use XML::LibXML'); (without checking it for errors) when you could just do use XML::LibXML; at the top of your script?

As for your problem, note that it is an issue with XSLT, not Perl, as you can verify by doing something like xsltproc -o output.xml transform.xsl input.xml at the command line. The problem is namespaces: note how your source document is in the namespace http://www.w3.org/2001/XMLSchema, but in your XSLT you don't take that into account. One way to do that is like this:

<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema" version="1.0">
<xsl:output method="xml" indent="yes"/>
<xsl:template match="xsd:File">
...
[download]

And using the xsd: prefix in front of the other element names too. But again, this is more of an XSLT question than a Perl question, so there are probably better suited forums elsewhere. See also the page XML Namespaces on w3schools, they also have a tutorial on XSLT.

Update: poj already posted while I was drafting.