How to test which version of TLS my .NET client is using?

If you turn on "CONNECTS" in Fiddler, you can see the TLS/SSL version in Inspectors -> TextView

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To turn on Connects, go to Rules in the menu bar and remove the check from "Hide CONNECTs"

Note: Decrypt HTTPs traffic must be disabled

Reference: Viewing HTTPS Handshakes in Fiddler

If you capture the connection creation in Wireshark, and examine the first packet from the client, then Wireshark will annotate the fields in the ClientHello struct for you, including the TLS version requested by the client.

Similarly, if you look at the first reply packet from the server, then Wireshark will annotate the fields in the ServerHello struct for you, including the TLS version settled on for the connection.

See this blog post or this one for worked examples.

The System.Net tracing does include sufficient detail to check this, although it's not very accessible.

This KB describes how to turn on System.Net tracing.

This blog post shows a full HTTPS request in System.Net tracing.

The bytes sent over the wire are logged, and in the example given on that blog post, the client stream starts:

System.Net.Sockets Verbose: 0 : [3848] Data from Socket#48285313::Send
System.Net.Sockets Verbose: 0 : [3848] 00000000 : 16 03 00 00 41 01 00 00-3D 03 00 43 26 02 90 83 : ....A...=..C&...

RFC5246 describes TLS 1.2 and explains that ClientHello is the first message expected and states its format:

  struct {
      ProtocolVersion client_version;
      Random random;
      SessionID session_id;
      CipherSuite cipher_suites<2..2^16-2>;
      CompressionMethod compression_methods<1..2^8-1>;
      select (extensions_present) {
          case false:
              struct {};
          case true:
              Extension extensions<0..2^16-1>;
      };
  } ClientHello;

This SO answer explains that the record starts with 0x16 as a type marker, then the protocol version.

The session shown above has version 3.0, which means SSL 3.0.

The RFC explains that 3.3 is TLS 1.2.

So if your client data starts "16 03 03", then your client is attempting to negotiate TLS 1.2.

You may need to examine the ServerHello to establish which version was actually used.