Official Backstory:

Set on Earth in the year 2065, destruction and confusion surround us. Cities are deserted, the population is decimated, and the precious few humans who remain must find a way to survive.

In this world, we face death as we part with our loved ones. We begin to question what "life" and "love" is, and what is the philosophical definition of the "heart." After all in this world, science has analyzed life and death, expressing life as a form of energy.

Beyond the riveting battle scenes, Final Fantasy will take you on a journey of personal discovery into both the real and fantasy worlds, drawing you deep into its characterizations and themes: love, friendship, dreams, adventure, life and death.

Summation:

Set on Earth in 2065.  A meteor has crashed onto the Earth unleashing aliens called phantoms who devastate the Earth (like the Lunar Cry from FF8).  The survivors of the initial onslaught (first impact!) move to barrier cities for protection.   However, time is running out for the humans.

Dr. Aki Ross is Earth's last hope.  With the help of Dr. Sid (her mentor) and Grey Edwards (captain of a DEEP EYES military squad), she races to save the Earth.  Aki gets terminally infected by an alien, and she holds the key to defeating them.  Unfortunately, Gen. Hein wants to use a massive cannon (like the Sister Ray in FF7??) to blow up the aliens and possible the Earth.  Aki searches her dreams for clues and the Earth for eight spirits who she believes will save the planet.

Theme:  life (common theme of saving the planet ^^)

This is all they story you're going to get here- don't think anyone wants it totally spoiled (inluding me!) ~_^