This wouldn't solve your problem quite as elegantly as what Franck is suggesting, but it would be an incredibly fast implementation for the meantime.
Create an HTML file with the following code (feel free to customize as needed):
<html>
<head>
<title>nothing</title>
</head>
<body>
<form>
<input type='file' size='50' />
</form>
</body>
</html>
Now, save this somewhere, and add it to your form "Resource Files", by going to Tools -> Resource Files -> Add..
Now, enable this HTML files as the custom taks pane, by going to Tools -> Form Options -> Advanced -> Enable Custom task pane.
Now the task pane will be there with a browse button. Click the browse button, "open" the correct file and the filepath will be automatically generated in the HTML text field next to the Browse button. Simply copy paste this filepath into the form field that you have set up and viola!
I'm not sure b/c I haven't really worked much with interaction between task pane and form, but there is probably a way to automate the copy paste from the task pane filepath to the form filepath.
Hope this is helpful!
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Matt Faus
Matt Faus / Microsoft InfoPath MVPQdabra® Software / Streamline data gathering to turn process into knowledge