Hi, I'm having the same problem with the datepicker on my contactform7 form as well.
I've tried deactivating/reactivating it, but it doesn't work.
I've also selected a theme from the form settings page (Redmond) and have saved it, but it still doesn't work - even though I've selected a theme and saved it, the datepicker appears to not be saving my changes (it still looks like the "Base" theme). Not sure if there's a save issue that's causing the datepicker to appear below the footer.
I'm using the latest versions of WordPress, ContactForm7 and ContactForm7 Datepicker plugins.