The airline company FrenchBee has a low-fare website for every city they fly to. For example: https://us.frenchbee.com/en/paris/flight-san-francisco-to-paris/low-fare-calendar.
If you are on a budget this is usually one of the cheapest direct flights options for NY/SF from/to Paris.
Here you will find the "Low Fare Calendar" to go from "San Francisco" to "Paris Orly". In the case you want to buy tickets to NY just change it like this:
https://us.frenchbee.com/en/paris/flight-new-york-to-paris/low-fare-calendar
And if you want to check for flights to paris just change the origin like this:
https://us.frenchbee.com/en/san-francisco/flight-paris-to-san-francisco/low-fare-calendar
So basically the template is:
https://us.frenchbee.com/en/[origin]/flight-[destination]-to-[origin]/low-fare-calendar
If you prefer you can also check prices in euros directly by using: https://www.frenchbee.com/fr/san-francisco/vol-paris-san-francisco/calendrier-des-tarifs
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