I've got a certificate with following cipher EDCHE-RSA-AES256-GCM-SHA384 ...
A certificate does not come with a cipher. It comes with a public key and the type of key restricts a bit which ciphers can be used (i.e. ECDSA vs. RSA authentication, RSA key exchange). The usable ciphers are instead depend on the TLS implementation and configuration in client and server.
All *-SHA384 ciphers are defined only with TLS 1.2. This means to use this the protocol version supported by both client and server must be TLS 1.2. Any client not offering TLS 1.2 or later in the TLS handshake will not offer this cipher and a server which does not support TLS 1.2 will not have implemented this cipher anyway.