Should a verdict against Google be returned, there's the possibility of some serious arm-twisting, and possible fiscal penalties which could be levied not just by the CNIL, but by other European regulatory bodies.
CNIL president, Isabelle Falque-Pierrotin, told Reuters that: "All options are on the table. We are not totally satisfied with their responses so we have set up this meeting to discuss the issues with Google."
She added: "We want to untangle the precise way that specific personal data is being used for individual services, and examine what the benefit for the consumer really is."
A Google spokesman said the company was happy to discuss the issue. He said: "The meeting will give us chance to put things into context and explain the broader actions we are taking to protect our users' privacy."
The CNIL's probe could see a result announced next month, but it may well take longer than that to untangle the ins-and-outs.
Google is under fire from all sorts of angles at the moment, facing accusations of anti-competitive action in the EU already, not to mention the US, over rival search engines and how it ranks them. And indeed India was recently rumoured to be engaging in an anti-trust investigation.
There's plenty to keep the Mountain View legal team going, then.