Russia has cheap energy and abundant natural resources, but lacks industrial capacity. Europe needs both, and has decent industry. There is mutually beneficial trade.
The US has the world's strongest military. The US offers Europe military protection in exchange for military access and political sway to maintain its position as the global hegemon. In exchange, Europe gets to export its goods to the US, backs up the US on the world stage, and Europe profits from a trade surplus. It's win-win.
A Europe-China deal has neither of these. China does not have abundant natural resources to export. And China will never provide military protection to Europe. And China does not need anything from Europe. The best Europe can offer is market access, to buy Chinese overproduced manufacturing, but that will decimate Europe's industry. Europe doesn't have an equivalent good that China needs, so it will run a trade deficit, which is a losing trade in the long term. It's win-lose: China wins, Europe loses. A relationship with China will never provide the same level of benefits as Europe's relationships with the US or Russia.
Any idea of Europe replacing its relationships with a new one with China is a short sighted knee-jerk reaction.