This issue has been discussed a few times on this forum, and some people found solutions like this:
Today, I contacted my host provider and asked them to enable allow_url_fopen, but they replied:
Unfortunately, for security purposes, we do not allow
allow_url_fopenon any of our Shared Hosting servers, as an example:
What are PHP allow_url_fopen security risk? - Information Security Stack Exchange
Is there any other workaround for this?
Hi @Richard_Honey,
unfortunately, the form submission only works when allow_url_fopen is enabled.
As a workaround, you can use a third-party form with an embed code.
Thank you Martin.
I was thinking Jotform inside an iFrame? Will that work?
Yes, it should work, but make sure it looks good on every device.
UPDATE:
Eventually, I found an acceptable solution: Web3Forms.
This service is the only one I could find that does not have any branding like Jotform , Typeform etc.
Also, it’s extremely easy to use - simply request a code (one per email address), copy the form code and paste into an html element in the Sitejet builder.
The only downside to Web3Forms is a maximum of 250 submissions per month (not bad), and a forced redirect upon form submission (for free users).
This is not a major issue, since you can edit the redirect page to any custom url. I created a simple success page as my redirect.
PS: @Martin, it looks good on every device! 
This sounds fantastic. Are you able to upgrade to more user than 250 submissions with a plan?
Yes. From $8 per month you get unlimited submissions:
web3forms.com/pricing
but I think 250 is enough for small businesses starting up.
It is. Thank you.