I did test and a user without SharePoint license can upload a file in the Microsoft form.
A user without SharePoint license:
Result: The upload file will be stored in the OneDrive of form creator.
In the Microsoft form, only internal user in the tenant can upload files.
Make sure you choose Only people in Contoso can response and copy the sharing link to the user.
Whether this issue occurs in all unlicensed users? Does is work well for the licensed users?
Please use another PC or browser to test.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.