How much do European PhDs care about GPA? I have an undergrad degree in field A and have a lot of skills that led to me doing research in field B (not a lot of crossover traditionally, but the lab skills are similar and the experiments I run in field B are improved by the lab techniques I have from A). 

I am now a fulltime research assistant at a top 10 university and have done interesting work including introducing methods from A to our work in B and proposing experiments grounded in understanding the science of B. 

I want to do a PhD, but the trouble is I have an undergrad gpa of ~2.0, and my degree is in field A. (I also did several years of undergrad research in A, including some pretty advanced work, in a top 20 department.) I will have glowing recommendation letters from some top names in B because of my research work. 

I want to do a PhD and a lot of people have suggested Europe because they're shorter. Do they care as much about gpa as American PhD programs? If so, I think it might not be worth applying because of GPA.
There are a number of relevant differences between North American and European PhD programs. First, it is key to note that practices differ greatly from country to country. The following answer will focus on general trends across Europe, but be aware that there will be exceptions.

One big difference is that in Europe you generally would not be applying to a PhD program, but for a specific position with a specified group/professor. As such there are typically less requirements set by a graduate school (such as a minimum GPA) to deal with. Since there is typically only one position to fill, the hiring tends to be more risk averse, and things like recommendation letters become more important than pure grades. People will still however look at the grades and a 2.0 GPA will certainly raise some eyebrows.

Another difference (also mentioned in other answers) is that in continental Europe, it is typically expected that PhD applicants have already obtained a Master's degree. It is very unlikely you will be hired without a Master's. The only exception to this (I know of), is the UK where it is more common to start a PhD directly after the Bachelor (and PhD's have a short nominal length of three years to boot.)