How many miles, err, kilometers? Check the usual things, tires, brakes & rotors, the steering head moves smoothly side to side, no evidence of front fork leaks, rear suspension does/doesn't damp well (aftermarket shock?). Because of the way Yamaha has done the front brake reservoir the fluid will appear black, just be sure that it is full. The transmission should shift smoothly from gear to gear. The FJR does go THUNK when initially shifting into first gear.
Ask when the last valve check/adjustment was done. (And, do you have any documentation such as shop slip or receipt.) The check is only done every ~42k kilometers but the check and especially the adjustment is expensive.
Listen to the left side of the engine, near the exhaust/cam area when it is warm, you don't want to hear a rattling sound, sometimes described as a ticking noise(1).
If it is a private sale see if you can find out from the owner if the bike sometimes feels like it has a little miss when accelerating hard in second gear, or perhaps better, ask if the owner notices anything unusual when accelerating hard in second gear(2).
Check the clutch lever by slowly pulling it in and letting it out, it should move smoothly, easily and should not have a notchy feel at any point in the pull and release(3).
One key should work everything. Ideally, the seller will have 2 keys and a key tumbler that is to be installed in a Yamaha trunk. Oh s#hit, if this Canadian FJR has an immobilizer be sure the owner has the RED key. If the motorcycle has an immobilizer but the owner does not have the RED key, that would be a near deal breaker.
If you do purchase the bike, stop back and we can recommend some maintenance items that are often overlooked that you really do want to have done.
I'll pile on with the others in previous posts, the FJR is a handful with its weight and power, R E S P E C T I T. Some have started out with the FJR as their first bike and both bike and owner have survived the experience but that doesn't mean that it is recommended. Even as a second bike after some experience on a 250, the FJR still isn't recommended as the next step.
Look over the suggestions in this thread. You may want to call the seller and ask them about some of the inspection things we have mentioned before driving 4 hrs to look at the bike.
(1) A few '03 and '04 FJRs had valve stem seals that were too tight which starved the valve guides of oil which led to wear. The valve stems rattle in the guides creating the noise I suggest you listen for. When the valve stems start to rattle some oil will start to migrate into the headers and when the wear is extreme oil can be seen at the exhaust pipe tips. A motorcycle with this condition will run perfectly fine and it will be reliable but eventually, due to oil consumption it will need to be fixed which requires the cylinder head to be removed and sent to a machine shop for new guides and revised stem seals.
(2) Not unique to the FJR can be second gear issues due to bent shift forks or worn gear dogs (that locks the gears together). In the very rare cases where there is damage, under hard acceleration only, it will start out feeling like an engine misfire as the gears pop out and back together again. As the damage progresses it will get to the point where the gear simply pops out and disengages under hard acceleration. This is something you should not try yourself if you test ride the bike because the FJR is a ferocious beast in the lower gears and you are unprepared for what a FJR can do right now. Really! If you ask the seller if it pops out of gear they most likely will give you an answer you want to hear.
(3) This is a minor thing, if the clutch lever feels rough or notchy it is a very simple and inexpensive fix, don't let it bother your buying decision. The brass bushing in the lever pivot can gall if not maintained and causes a feel issue. This is one of the common overlooked maintenance items.
