Last month, the French privacy watchdog, CNIL, ordered the firm to extend people's right to have posts removed from its websites worldwide, including Google.com.
Google said it "respectfully" disagreed with CNIL's authority to make such an order.
The firm now faces possible fines.
A 2014 court ruling allows Europeans to submit applications to Google to remove data from search results that they thought were out of date, irrelevant or inflammatory.
Google is believed to have processed more than one million requests to remove data since the ruling came into effect. It reviews all requests and refuses those it judges have no merit.
However, those that are deleted are removed on its European websites such as Google.de or Google.fr. They are not removed from Google.com.
The company points out that more than 95% of searches in Europe are made on the firm's local websites.
In a blogpost, Google's global privacy counsel Peter Fleischer wrote that the French regulator's request was a "troubling development that risks serious chilling effects on the web".
"While the right to be forgotten may now be the law in Europe, it is not the law globally," he continued.
"As a matter of principle, therefore, we respectfully disagree with the CNIL's assertion of global authority on this issue and we have asked the CNIL to withdraw its formal notice," he added.
The CNIL said it would look into Google's appeal and make a decision in two months on whether to accept it.
"We have taken note of Google's arguments which are mostly of a political nature. The CNIL, on the other hand, has relied on a strictly legal reasoning," a spokeswoman said.
