Europe consist of many countries but there is only one car seat standard which is called ECE R44. Car seats must be certified with this standard or they are illegal. It's not legal for foreigner to use a US car seat in Europe, doesn't matter if it's for a vacation of one day or whole year.
but then this really brings up the big question--how can something be illegal throughout Europe, when laws are generated within the borders of each individual country?
Car seat laws are not generated within each country. Countries have made small tweak, such as minimum requirements for seat belts. Car seats must be certified ECE R44 which is why fore example Sweden had to phase out the older Swedish T-standard from the 1970's. Interestingly, this standard was stricter than any car seat standard globally except the brand new Swedish "Plus Test".
The law basically says anyone under 135 cm tall (53 inches ) must be in a car seat restraint of some kind. Some countries have made small changes to this rule, a bit stricter, but it's details.
Like other posters said the risk of anyone noticing is basically zero. It's just like using a European car seat in US.
I personally think anyone bringing a car seat on a trip is doing a great thing and really thinking of car seat safety ahead of time. Who knows what seat you wll be stuck with over there? Please double check with your airline before flying since there are so many rules regarding using car seats on planes. This is usually more an issue when traveling back to US.
Misuse in Europe is just like in US huge although some countries are better than others.....
Have a nice trip!