Joining an arc affiliated automotive club is indeed an option. I choose different because the logistics are usually organised on a country base. What I mean with that is that in case of a break down, you need to contact the club you joined, who will then arrange help. Sometimes that help is not always a local garage, but a representative of your club in that country. For example, both the Dutch and Belgian automotive clubs have satellite stations in France. They are usually based in the South and take care of all calls from all over France. This way of working can take quite some time before your car is fixed. It is not uncommon to spent more then 3 days to get your car fixed. An alternative is to join europ-assistance.<hu/co.uk>. You still need to contact your local branch, but they seem to have better internal communication lines, probably because they are from the same holding.
Further more it might be worthwhile to check local initiatives. In Belgium for example you get breakdown coverage for three weeks when you buy gas at total (Only French and Dutch unfortunately). They claim to cover Europe.
Finally it is worthwhile to check you car insurance , some do provide European car breakdown service.
Also, be really explicit when you take breakdown service, most plans provide coverage of an old car at an extra cost. Without that extra you. Are not covered, even if you paid the standard fee.
Also I am afraid you are bound to register with an organisation in the country where your car is registered. It is said that there is a common European market, but from my experience that is not applicable to banks and insurance's.