A UK driving licence is automatically valid in any EU country. Similarly, a UK insurance policy automatically provides cover for the minimum legal requirements in any EU country. (Note that the minimum requirements are typically the same as the UK requirement for 3rd party cover. So, if you've got a 'fully comp' UK policy, it will give you 3rd party cover when driving your car abroad but little else).
Many European countries have laws which require drivers to carry safety equipment, such as a fire extinguisher, first aid kit, high-vis vests (one for each person in the car), a warning triangle and spare bulbs. Since any sensible driver carries those anyway, it shouldn't present much of a problem.
Some countries have speed limits which are automatically lower when it's raining. France has a 'priority from the right' system, which means that (unless there are signs to the contrary), a driver entering traffic from aside road has the right to pull out in front of you; you must give him right of way.
One of the most frequent errors, made by British motorists, is to forget that you travel
anticlockwise around roundabouts when abroad.
As far as hiring a car goes, most of the big firms won't let you do so (in any country) unless you've held your licence for several years. That's because of exclusions in the insurance policies of the hire companies. However, small operators in major resorts might be more flexible. (Many companies also have a minimum age for hiring a car. This can typically be anywhere between 21 years and 25 years).
For much more information (including the rules which apply in specific countries), start here:
http://www.theaa.com/motoring_advice/overseas/ index.html
Chris