You can argue that Spain is the biggest colonial 'loser' in that most of its colonies have been lame duck states that only prospered in recent times, and during the times they had them, failed to extract wealth efficiently or effectively while other states made mints out of a few Caribbean islands alone. But they did leave behind a legacy of over 400 million native speakers of their language that have strong cultural ties to Spain; as these states become more prosperous in the future, Spain's legacy will be felt far stronger. Empires come and go, but the impact of their actions is felt forever; which is why ensuring French success in colonization is IMO a cornerstone of a true wank, even if decentralization of the empire by rebellion or dominion is likely inevitable.
As outlined above, there's a window for Columbus to sail under the French flag and what will absolutely determine the nature of French colonization is discovering gold. To hell with OTL, gold is gold and you can be sure to draw settlers like mad if you can use it as bait. Potosi had 30,000 Europeans relatively shortly after conquest due to striking gold. California's population boom can be attributed entirely to the gold rush, which laid a foundation for American presence on the west coast far faster than it would have been otherwise. So what matters most here is likely the discovery of gold by the French, before its competitors. IIRC, the nearest source of gold is probably in the Hispaniola although its sources quickly drained dry. That being the reason conquistadors became a thing, moar gold.
Columbus is unlikely to strike gold or be anywhere near Hispaniola on his first voyage, and more likely to end up in the American South. Which means that you're likely to need a return voyage after a not-so-successful one for Columbus to discover the more prosperous brand of native found in the Caribbean and Mesoamerica that possess gold.