JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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While editing your form, click on the file upload field, then click on the little gear icon in the top right corner of the field to open the options. From the options menu for the upload field, change allow multiple to "Yes", then change maximum number of files to "1" so that is a single file is still allowed. After allow multiple is enabled, the option to change the button text will appear:
Change the button text to whatever you would like.