Hey jvthomas21,
I did some research on Microsoft SQL managed by Azure. The TLS version that the DB requires is set at the DB level, while the JDBC Driver will have its own TLS version. Its important to make sure the correct driver is in-use. My guess is that the Driver is using an older version of TLS.
You could try installing a new driver, and connecting with the appropriate encryption as described here by Microsoft.
Regards,
Wali