Hi!
I had the same issue. But when I downgraded jquery.form.js from 2.94 to 2.87 my issues had gone.
It’s just new version of jQuery plugin fault.
To resolve this issue you can download “Contact Form 7” plugin, version 3.0.1 and just replace existing jquery.form.js with this old one.
Have a fun! Happy New Year!
This worked like a charm! Thanks so much!
http://wordpress.org/support/topic/attachments-and-file-uploads-not-working-in-contact-form-7#post-2534325
You should really try this, guys.
Replace (e.g. via FTP) the jquery.form.js file in the plugins/contact-form-7/ folder with the older one, which you get from this thread I linked.
This worked perfectly for me.