Hi David:
Many years ago (2004, perhaps), I took my motorcycle from the USA to Europe on the Cunard ship 'Queen Elizabeth II'. To the best of my knowledge, this was the last regularly scheduled ship on the Atlantic run that would accept vehicles. It was not cheap, in fact, it cost me far more to move myself and the motorcycle to Europe on the QE II than it would have cost to move myself and the moto on an airline.
I researched the whole issue of moto transport on ships doing the trans-Atlantic run very carefully back then, and the QE II was the only ship I could find that offered vehicle service. I don't think anyone else has stepped in to fill the gap, the QE II having been decommissioned several years ago.
Maybe -
just maybe - you might be able to find a cruise ship company that is willing to take your moto along if you buy passage for yourself on one of the trans-Atlantic 'positioning voyages' that take place in the spring and fall when the cruise ship operators move their vessels from the Mediterranean to Florida/Caribbean and vice-versa. You would need to contact the cruise ship companies individually, I know for sure that none of them advertise such a service.
However, I don't hold out a lot of hope for this. The cruise ship companies are not set up to handle customs clearance at either end of their voyages for anything other than passengers and their baggage, and my guess is that they would be unwilling to take the risk of encountering delays or problems arising from carrying something that they are not familiar with - namely, a motorcycle.
It would be far cheaper, faster, and more trouble-free for you to air freight your moto from London or Paris to Toronto or Montreal. I've done this numerous times using
Motorcycle Express. They are not cheap, but they know what they are doing and they are very attentive to the details - you will not encounter any surprises if you ship with them. It is to your advantage to arrange to be on the same plane as the moto, because this will minimize the storage charges (typically about $50 a day) that are imposed on the moto while it is in the air freight shed at the destination.
The "trick" that Motorcycle Express uses is that they book cargo space on charter carriers (typically Air Transat, a Canadian carrier) who are operating wide-body aircraft. These carriers usually fill up the passenger cabin, and the passengers have two suitcases each, but the carriers don't have much air cargo business, therefore, there is lots of empty space available down below. A motorcycle weighs 'nothing' so far as the airline is concerned (it fills a container that is designed to carry 5 tons), and the carrier needs to move the empty containers around anyway, so moving a container with a moto in it is, in the airline's opinion, like getting money for old rope.
Your FJR is pretty much the same size as my ST1100 - see the photo below to get an idea of how to pack it. No need to drain the gas or disconnect the battery or anything like that, just show up with less than 1/4 of a tank of gas. Motorcycle Express arranges the ULD, the pallet, the straps, the paperwork, everything.
Basically, you drop the moto off the day before the flight, then pick it up at the destination freight facility the same day you arrive. Best I ever did was land at Paris at 6:10 AM and was on the road riding away from the freight facility a couple of hours later at 8:30 AM.
Michael
Motorcycle in ULD (Uniform Load Device)