Ethnic enclaves are a fact of a heterogenous society, they're not a sign of problems in an of themselves. The problems arise when the various cultures and ethnic groupings feel as if there is resource scarcity and begin retreating to their distinctive corners, but again, the problem in this scenario isn't the fact of different groupings, it's the resource scarcity. No matter how homogenous a society is, resource scarcity will turn brother against brother.
New York City is the principal city in the world, serving as the financial capital of the global hegemon. Like all of its predecessors in this regard, the incredible diversity of languages present in the city is a feature, not a bug. If you were to walk the streets of Rome in 115AD or Constantinople in the 16th Century or London in the 18th Century you would also hear multiple languages being spoken. The fact that NYC has that position in the age of globalization has just supercharged that phenomenon. If you were to snap your fingers and make NYC a unilingual city it would collapse in prominence and relevance overnight. Everyone calling NYC home should have one shared identity - be it as New Yorkers or as Americans - but that does not mandate the exclusion of their other identities - be they ethnic or linguistic. Canada, for example, has long prided itself on rejecting the melting pot framework, instead considering itself a salad bowl or cultural mosaic.
The Anglo-Franco tensions in Canadian history aren't due to the variety of languages that are spoken, it's more or less just run of the mill civil tensions when two large ethnic groups dominate a national project. Toronto and Montreal are each incredibly diverse cities with multiple languages being spoken, yet there is no notable intra-city ethnic tensions. The tension is at the national level between two ethnic groups, and are as much related to religion (Catholic vs Protestant) and power politics as it is to language.