There are no marriage applications in St Louis before the 1880's as they were not required by law.
Your only hope is getting the full marriage record that should give the name of the minister or justice of the peace who performed the marriage and if you are very lucky, the name of the church
where the wedding took place. If it was a Catholic marriage, then the Parish Marriage register will have names of the parents of both the husband and wife. Having just the minister's name will take further research to find out exactly which church he was attached to that would have the marriage registers.