New York will reap a state budget windfall of at least $3.3 billion in fines paid by the big French bank BNP Paribas after it pleaded guilty recently to violating sanctions against transactions in Cuba, Sudan and Iran.

So, how should the money be spent?

Consider this analogy:

You and your family live in a big old house that needs tens of thousands of dollars in repairs. Your income is pretty good, but you live paycheck-to-paycheck.

After taking out a home-equity loan and maxing out your credit cards to fix the leaky roof and rotten clapboards, you’re still occasionally borrowing more just to pay the guy who cleans out your gutters and plows your driveway.

You learn one day that a distant cousin has died and left you $3,000. It’s not a life-changing sum, but it gets the family excited.

Your teenage son reminds you that upgrading to the premium cable package would allow you to watch more ballgames together. Your spouse and younger kids would love to cool off in a backyard pool. Your brother-in-law wants to reduce the rent he pays for his room above your garage.

Still, you can’t help thinking about how overextended you’ve become to pay for the upkeep on the house — and the work that still needs to be done.

This is essentially the sort of challenge facing Gov. Andrew M. Cuomo, whose next budget will recommend how the BNP Paribas cash shall be appropriated by the legislature.

Simply splurging — say, tossing the lump sum at schools or giving it away in tax cuts — would be shortsighted and irresponsible. Once the cash is spent, Cuomo would have to find it somewhere else, and he’s already promised more than he can deliver over the next four years with cutting projected spending.

The right choice is pretty clear.

New York State, like the cash-strapped owner of an old house, has massive ongoing infrastructure needs — and, as it happens, this is a perfect time for a fresh infusion of money to help meet them.

The five-year capital plans for the Metropolitan Transportation Authority and state Department of Transportation expire at the end of the fiscal year. The 2016 budget the governor will present in January should show how the state will help fund those programs.

Cuomo should evenly divide the BNP Paribas money between the MTA and the DOT capital plans. The top priority should be to find ways to permanently reduce New York’s reliance on borrowed cash to cover recurring maintenance needs and reconstruction of highways and bridges.

In the MTA’s case, that would mean targeting it to the “state of good repair” budget for the rail and transit system.

In DOT’s case, Cuomo should consider targeting the money to the Consolidated Street and Local Highway and Improvement Program, which supports improvements to local road systems in every corner of the state. The debt service on bonds floated to finance the program now almost equals the total annual expenditures of the program.

This approach would have double-barreled benefits for Long Islanders, who use both the MTA and the roads eligible for CHIPs money.

To be sure, the $3.3 billion in BNP Paribas fine money would represent a small share of the total needed to finance the next MTA and DOT five-year plans, which are likely to total more than $25 billion each.

Nonetheless, making strategic use of this money to support New York’s undernourished capital infrastructure plans would yield the greatest lasting benefits for all New Yorkers.