You can't add an 'attachments' field to the standard Shopify contact forms.
You'd need to use one of the following apps, to make a new contact form (with attachments) which would replace the built-in contact form that your theme came with:
It's not possible to do it via coding.
The Hulk App (https://apps.shopify.com/form-builder-by-hulkapps) has a free plan though, which allows for File Uploads.
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