In an exclusive interview with the Guardian as Google's new privacy rules came into effect, Reding said: "Any company which wants to utilise the European market of 500 million citizens - which we've made borderless, a golden opportunity - then the European rules apply."
She said that if people gave up their privacy, it should be done in full knowledge, and not by "sneaking" it away.
Google faced widespread criticism as it implemented its policy at midnight on 1 March, uniting its code of practice across up to 60 services including Google Search, YouTube, Blogger, Gmail and others.
Late on Wednesday night it emerged that the French data protection authority, the CNIL, had written to the giant search engine company on 27 February and said: "Our preliminary analysis shows that Google's new policy does not meet the requirements of the  European directive on data protection." The CNIL said it would lead a Europe-wide inquiry into the changes.
While they simplify the joining process for new users, the changes also mean that Google can pool data about signed-in users' web or video searches, map directions, web browsing, which ads have been clicked, and other information in order to target adverts and services at people using the web.
Google has a huge share of the search market in Europe, providing about 90% of searches across the continent - far ahead of the US, where its share is below 70% - and 97% of its $10bn (£6.2bn) revenues in the last quarter of 2011 came from "serving advertising" - ie placing advertisements on websites.