First, Eurail is the name of a pass which allows you to travel on the national rail systems of many counties.
In Europe, rail travel is very widely used, and the trains are often very modern and fast (some, such as the TGV in France, cruise at about 200 miles per hour).
Your question about safety is a little like asking if it’s safe to fly on, let’s say, Southwest Airlines. Having said that, some big-city train stations are located in slightly seedy neighborhoods (Rome,for example). I don’t mean dangerous, just seedy.
If you’re worried about transiting seedy neighborhoods at night, just time your arrivals/departures for daylight hours.

Where in Europe?  While I’d still probably travel alone in Romania, it’s a lot different and a little scarier than train travel in France.  All of western Europe and most of eastern Europe is perfectly “safe” for a solo female on the train. 

The main issue will be theft, which isn’t a huge problem but it does occur. So figure out a way to keep your belongings safe. For example, use a money belt to store your cash, credit card, and passport. That said, I like to keep another credit card in my regular luggage, in case of emergency. Be cautious about walking away from your luggage at train stops.

A good rule of thumb is to never let your bags out of your sight (when you’re awake; when you’re asleep on a train you can strap it to something, or yourself) You’ll see lots of Europeans just flip their bags up on the luggage rack and just walk away and sit 15 feet from it; I’d recommend against this []