Quick question, I'm planning to go to France for a trip for a few weeks and am I able to go to France without a Schengen Visa? I'm a US green card holder and a permanent resident here in the US. Not a US citizen though, my passport is from the Philippines.
The green card is irrelevant. It is your nationality (citizenship) that matters. As a Philippine citizen you need a visa to enter the Schengen area. Sorry.
A Green Card is a document allowing you to stay in the USA. It has no worth outside the USA.
To add to Chris's reply, your green card will allow you to use the US citizen's line, instead of the foreigner's line, when returning to the US. This can save lots of time. However, when you land in France, you'll be traveling on a Philippine passport, so those are the rules you have to follow.
I hope you have enough time to get your visa before your trip. If you don't have the correct papers, the airline will not let your board (they get heavy fines if someone is not allowed in, so they're quite vigilant).
I don't know where you reside in the US, but you will have to make an appointment with the French consulate responsible for your area in order to get the visa. I am posting a link below to the site of the consulate in Chicago to give you an idea of the process and timing.
http://www.consulfrance-chicago.org/Short-stay-visa-for-tourism-business-or-family-visit