You'll need to recompile the application against .NET 3.5; install a hotfix on the machines that run it; and change the code to enable TLS support:
Support for TLS System Default Versions included in the .NET Framework 3.5 on Windows Server 2012
Alternatively, you can upgrade your application to .NET 4.5 or higher. You will still need to either change the code to enable TLS 1.2, or set a flag in the registry on all machines where you application runs:
Enable strong cryptography in .NET Framework 4.5 or higher
if your application is running on Vista, Server 2008, or any earlier version of Windows, you cannot
support TLS 1.2 even if you install the hotfix.