The EU, which began looking into Google's search practices in 2010 and officially opened an investigation in 2015, brought charges against the company for allegedly prioritizing its comparative shopping feature while rival websites were pushed down the search result list.
The Luxembourg-based General Court, Europe's second-highest, is expected to take several years before ruling on the appeal.
The fine over Google Shopping broke the previous European Union record for a monopoly case against United States chipmaker Intel of 1.06 billion euros in 2009 and made the EU the global leader in regulating Silicon Valley giants.
The EU Court of Justice told a lower tribunal last Wednesday to re-examine U.S. chipmaker Intel's appeal against a 1.06 billion euro fine, dealing a rare setback to the Commission.
Initially Google was given 90 days to comply or face further fines.
While Google has appealed the decision, it has not requested that the court suspend it in the meantime, and it appears as though the company will continue to work towards fulfilling the changes ordered by the June ruling.
Google last week notified the European Union it would attempt to meet the demands of the European Union decision. Margrethe Vestager, the EU's antitrust chief, has also threatened further probes on travel or map services.
When reached by TechCrunch for comment a Google's spokesman declined to confirm whether it would be complying with the Commission's antitrust order while it pursues a legal challenge - or to answer any questions.
Brussels accused Google of giving its own service too much priority in search results at the expense of other price comparison services, such as TripAdvisor and Expedia.