The other thing you need to understand is that driving in europe is different than the US - or Canad

There are no rules about getting off an overnight flight and renting a car - but we have done MANY road trips in europe and while we often pick up the car at the airport we land at (arranged in advance with clear info on all taxes, fees and insurance) we never drive for more than an hour or 1.5 hours - just because jetlag can be very disorienting.
The other thing you need to understand is that driving in europe is different than the US - or Canada. Speeds are higher and people take driving very seriously. los angeles traffic ticket One does NOT drive in the left lane (unless los angeles traffic ticket stuck in hideous traffic) left lane is for passing only - and sports cars will pass you at VERY high speeds.
I strongly recommend los angeles traffic ticket either picking up the car your first full day - or leave yourself only a short and simple drive the day you arrive. Also - check everything on the car before leaving the lot - including locks, wipers and how to access the gas tank. Also - learn why type of gas you need - europe still has leaded gas and there is a lot of diesal and you don;t want to ruin a car engine by using the wrong one.
When flying into Frankfurt and collecting a car from the airport you have higher fees than if you elect to collect your car elsewhere. However I have heard of people collecting their car in Kelsterbach (just outside the airport) rather than from the airport itself, to save on the extra fee, although I have never done this myself (always have too much luggage to contemplate taking it all, and prefer the convenience of renting straight from the airport). You can take the S-Bahn (local train) line S8 or S9 from Frankfurt Airport Regionalbahnhof los angeles traffic ticket to Kelsterbach, and then there would be some bag-schlepping by foot to the car rental place unless you can find a taxi at the railway station. The S-Bahn takes about 13 minutes.
Unlike Canada, driving in Europe is a delight, just make sure you know when you have the right of way and when you have to yield. As a rule there are no head scratching, arm waving four way stops in Europe.
My preferred rental agent is Gemut, in Seattle. ( www.gemut.com ). They specialize in Germany and Austria, and they will arrange for a car for you with whatever rental cat company they consider reliable. If Kelsterbach is where Dollar/Thrifty are located, stay clear of them. On this and other travel forums, los angeles traffic ticket there are 100's of horror stories of people who have been taken advantage of by Terstappen, the agent of these two companies, in Frankfurt and Munich.
I assume you are returning the car to Frankfurt. There may be a (very large) los angeles traffic ticket drop fee if you don't return the car to the same country in which you pick up the car. Also, I would second Gemut, los angeles traffic ticket although I had (a very small) extra drop charge within Germany the last time I used them that they pleaded ingorant of. I have had good luck with Hertz- they have reasonable discounts if you are a member of AARP, Costco, AAA,some credit cards, etc. Be sure to have the car inspected for damage when you return it. I usually take pictures, especially if the return is not manned.
The car rental agencies at FRA rent to people all the time who fly in on an "over night " flight. However, I suspect they may be hesitant to rent you a car if you roll of the plane smelling like a brewery. The DUI laws are generally more strict than those on this side of the Atlantic, especially in Sweden, Denmark, and Norway.