No, for three reasons:
First, Rapier specifically states:
You can’t wield a rapier in two hands in order to apply 1½ times your Strength bonus to damage.
Second, Weapon Finesse allows you to use DEX mod instead of STR mod on attack rolls. Wielding a one handed weapon in two hands allows you to add to your damage rolls. Two completely different cases.
Third, you cannot use Weapon Finesse when wielding two handed weapons, or wielding a one handed weapon in two hands. There are a couple of specific items that change this ( iirc, Elven Courtblade from Races of the Wild and the cheesechain Spiked Chain ), but it is limited to those items.
For two-handed, reach weapons that you can use with Weapon Finesse, your options are basically spiked chain, and the drow scorpion chain (read: a slashing version of the spiked chain) from Races of Eberron.
Races of the Wild has several weapons that can be used with Finesse without being light, but none have reach. The lynxpaw is a double weapon (i.e. can be used as a two-handed weapon), and the elven courtblade just is a two-handed weapon. The elven thinblade is a one-handed weapon à la the rapier, i.e. it imposes restrictions on two-handing it.
Other rapier-like weapons include the ribbonweave from Races of Eberron and the quickblade rapier from Complete Adventurer.
The last such weapon I can find is the dragonsplit, from Monster Manual IV. These are one-handed but count as light for TWF and Finesse, and also have 19-20/×4 criticals. I’m not sure if they can be two-handed but since you’re not going for dual wielding I wouldn’t bother with them.
The spiked chain (or scorpion chain if you want slashing for some reason, or are a drow who can get easier proficiency) is far-and-away your best bet.
Alternatively, the feycraft template from Dungeon Master’s Guide II can make any one-handed weapon compatible with Weapon Finesse. It can also make light weapons use Dexterity instead of Strength without Weapon Finesse, which is often a bigger deal. I don’t know any one-handed weapons with reach, but the kusari-gama from Dungeon Master’s Guide is a light weapon with continuous reach à la spiked chain.
Best Answer
They are not mutually exclusive
And in fact there's even one weapon that's two-handed but finessable (the Spiked Chain). You can Power Attack with a finesse'd weapon as well, unless it's classified as a Light Weapon. Did the designers intend this? We'll never know, but the RAW is fairly clear on the matter.
There's no text in Weapon Finesse or the section on using a one-handed weapon in two hands that forbids it.