The 2008 European Commission fine - a record at the time - penalised Microsoft for failing to comply with the regulator's order four years earlier to provide information that would allow other products to work with computers running its software.
The software firm has since taken a more conciliatory approach in dealing with the Commission, highlighted by its decision to reach a settlement with the regulator in 2009 when agreeing let users of its Windows operating system to choose their own browser.
Rival Google Inc has adopted a similar tone in handling an EU regulatory probe of its web search practices.
The fine was "most undeserved", Jean Francois Bellis, Microsoft's lawyer told the General Court, Europe's second-highest.
"This case would not have arisen if the Commission had been as explicit with respect to rates which it wanted Microsoft to charge as it had been with all other terms of licensing proposed by Microsoft," he said.
The Commission argued that Microsoft's actions after a 2007 court ruling showed that it was able to identify within a short time the measures needed to comply with its order.
The General Court typically gives its verdict in six months to just over a year after a hearing. Appeals can be lodged with the EU Court of Justice, Europe's highest court, but only on points of law.
The odds would appear to be in the Commission's favour, said Christian Riss-Madsen, a partner at law firm O'Melveny & Myers.
"I would think, based on its track record, the court would be reluctant to overrule the Commission's fining decision, giving the Commission some discretion in its enforcement," he said.
The hearing will be watched by companies challenging regulatory fines, among them Intel, which has appealed in EU courts against a 1.06 billion euro penalty imposed by the Commission last year.
Microsoft's non-compliance penalty was nearly double the original 497 million euro fine the Commission imposed on the firm in 2004 for abusing its dominant position to thwart competitors.
Microsoft was supported in the case by the Computing Technology Industry Association and the Association for Competitive Technology.
IBM, Oracle, Red Hat, information technology lobby group ECIS, the Free Software Foundation Europe, the Software & Information Industry Association and software organisation Samba supported the Commission's position.