I'm a US green card holder and a permanent resident here in the US however I have a Philippine passport and am a citizen from that country. Do I need a Schengen Visa to travel to France for a few weeks, just a trip?
It doesn't matter if you have a green card or not, what matters is your nationality. This list says Philippine nationals need a visa.
You can use the green card to prove ties to your home country though!
A USA residence permit (green card) can only exempt you from having to get a transit visa. This won't matter for you as you are visiting and not transferring and Philippine citizens don't need a transfer visa anyway.