A spot check of The Azura in March found it was burning bunker fuel containing 1.68 per cent sulphur, above the 1.5-per cent European limit.
The court will delivers its verdict on November 26.
The Azura, capable of carrying more than 3,000 passengers, is one of the largest in the fleet operated by P&O Cruises, which is owned by Carnival.
The Mediterranean port city is grappling with the polluting effect of its drive to increase boat tourism.
The city has wrestled with increased smog in recent years, as it seeks to attract more lucrative cruise tourism.
Authorities say shipping could be responsible for 10 to 20 per cent of the damaging particulate matter in Marseille's air, which can cause respiratory problems and lung disease.
High-sulphur fuel, which is cheaper than cleaner versions, produces sulphur oxides which contribute to acid rain and the acidification of oceans.
Environmental campaigners say shipping is particularly harmful in Marseille, with fine particle levels 100 times higher near the city's bustling port than elsewhere in the city.
The UN's International Maritime Organization has been lowering the allowed sulphur levels in ships for years, with a new limit of 0.5 per cent coming into force in 2020.
But the NGO France Nature Environnement, one of the plaintiffs on the civil side of this case, says the new maximum is still too high.
Marseille registered 1.55 million cruise ship visitors last year, and officials hope it will surpass the numbers in Venice this year to become the fourth-largest port of call for cruise ships in the Mediterranean.
The city is aiming for two million cruise line tourists in 2020.
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