getting there from paris and the best place to start - please
Try https://www.rome2rio.com/.
You can fly to many cities from Paris. Next it depends on where you want to go: take a train to Marseille and the ferryboat to Ajaccio, or a ferry from Nice to Bastia.
Going from Paris flying probably makes the most sense. There are four airports in Corsica - but Ajaccio AJA is the biggest - and two main airports in Paris - Charles de Gaulle CDG and Orly. Protip: CDG and Orly are not near each other so avoid transferring between them if you can.
Are you going to be in Paris the city or are you looking to fly from one of the airports directly? Both CDG and Orly are outside the city of Paris so feel free to pick whichever has the flight that suits you best if you're coming from the city itself. You'll may have more choices flying from Orly which has more internal carriers and may more flights options. It looks like you can fly direct and it's less than 2 hours.
So figure out which airport in Paris you want to use and where you want to land in Corsica and the rest should be as easy as checking any flight.
Good luck,
=Tod
Corsica is most easily toured by car, but there's a very enjoyable narrow-gauge railway too that links Ajaccio with Bastia and Calvi. There are flights from Paris to any of these three towns, plus Figari near Bonifacio (a small town that looks beautiful, but I've never been). Also, take your hiking boots: the island is a hiking paradise.
I suggest you get a copy of a Corsica guidebook to narrow down what you want to see: the island isn't huge by land area, but transportation is extremely slow going due to the terrain.