I tried again with last openssl version 1.0.1e this time (instead of 0.9.8n).
openssl ecparam -out ec_client_key.pem -name secp384r1 -gen
openssl req -config openssl.cnf -new -key ec_client_key.pem -out ec_clientReq.pem -sha384
openssl req -in ec_clientReq.pem -noout -text
Now I get the expected result:
Signature Algorithm: ecdsa-with-SHA384
It looks that version 0.9.8n does not support sha384.
This extract from the CHANGES file seems to confirm this:
Changes between 1.0.0h and 1.0.1 [14 Mar 2012] : ... *) Add HMAC ECC ciphersuites from RFC5289. Include SHA384 PRF support. As required by RFC5289 these ciphersuites cannot be used if for versions of TLS earlier than 1.2. [Steve Henson]
Thanks gtrig for your help.