All insurance will cover EU countries. You will have the list of included and excluded countries in your policy documents. Enquire with your insurance for the need of green card.
You need to remember to take your bike's documents as some countries will ask for this (Vo5).
What you really want to make sure you have is the breakdown cover.
STAY AWAY from addon from insurance companies as they will rip you off, what they offer is never what you need.
Greenflag have nice prices for EU breakdown cover and allows for multivehicle cover.
All the other big players will have similar EU cover.
unless of course you are travelling outside the EU, then you have to make your search to fit.
Another thing to consider is the city centre green tax (each country have different names).
Like OLEZ in the UK most countries will have limits for what type of vehicles can circulate in city centres.
I always carry with me a bulb replacement kit, French are always changing their laws regarding highviz and breathalyzers, for the cost of a couple quid isn't worth the hassle so I have a pair too.
The obvious GB sticker..