If there's a particular reason the users of the site would want to send images (e.g. screenshots for bug reports or support), then I would re-label the file-upload widget as something like "upload image" for the mobile version of your form while leaving the desktop version unchanged.
On iOS, a standard HTML file-upload widget triggers an action sheet that lets you take or choose a photo, so with the re-labeling you'd be all set.
On Android, it seems that hitting a HTML file-upload widget gives you a choice to upload photo, video, or from "Documents," and choosing "Documents" exposes files from your cloud drive and downloads in addition to images and such, but nevertheless, a user wanting to upload from those places through their Android device seems like a pretty limited use case.
In general, I'd say that uploading an arbitrary file through a mobile device is a pretty esoteric task for most users. Heck, it is for me, and I'm supposed to be a UX guy.
So in sum I'd say that re-labeling the widget to "upload picture" could work, as taking & sharing pics and traversing the camera roll are well-worn tasks for most mobile users. But if there is not a particular reason that it's important for your users to upload images, I would consider omitting the document upload widget from the mobile version of your form entirely.