Thanks for your answer.
I haven't got a crossed cable right here so can't do a direct connection, but I will find one.
My FAE told me that the constraints used for the design assert that the clock is centered around the data, which may need a special configuration of the PHY. Because I would avoid to modify the Linux kernel, I may have to change something in my clocks, but I don't know enough on hardware for that.
My dev workstation is an old RHEL5 and I have only tcpdump. I will try also to find Wireshark that should give me more info on the errors...