A VPN is just like a tunnel between your city to the other city in which you want to deliver the message. Let's assume that you are a message carrier, and you are having a text to deliver. For security, you'll use a tunnel, your VPN is in short tunnel will protect/hide you to the people who are going to steal information through you.
But encryption is something like other thing.
We can say that encryption is something you know the message in some code-word. You only know the code of the message and you know the person you are going to deliver the message. The writer knows the encryption technique and decryption both. Here encryption means how you generated the code of the message you are going to deliver. Decryption means how to convert code-word to the original message.
What will happen if someone steals code-word from you? Nothing. Your code-word will not be useful unless he knows the decryption technique.
It is called security.
One thing more, I don't think any mail services like Gmail, tell anybody how they encrypt and decrypt. In general, nobody knows how the generated code form your given data, and your mail domain holder knows both techniques. When you compose an email it is encrypted for security reasons by the mail domain and then it is sent. Then it is decoded.
So it is not necessary for both of you to use the same VPN.
The other thing if VPN encrypts your data, that means he also knows how to decrypt it, and they will give the data to your mail holder according mail encryption. In this case, double encryption will be used first for mail domain and second for VPN.