Two songwriters, Sami Chokri and Ross O'Donoghue, allege that Sheeran's song has musical similarities to one they wrote called "Oh Why".
The decision on Monday by the country's highest court not to hear the case definitively ends the legal challenges which had been closely watched by the music industry.
The rules, aimed at tech giants, address the growing role of online platforms, and will force them, if adopted, to share revenues with publishers and bear liability for copyright infringement on the internet.
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