We feel quite blind in how to best help her. If she decides to get a cheaper android with service, would it be a smart phone able to link into some of her apps?
She could certainly buy a smart phone over there. Yes, she should be able to install most of the same apps she had on her old phone (assuming it was an Android too). Google uses the Google Play store for apps, and which apps are available country to country may vary - but most of the common apps she surely used ought be available in Europe from the Google Play store in which ever country she activates the phone in. Or, Google may base that on her original Android account and direct her to the US Google Play store anyway - not sure. But...yes, almost certainly, all of her old apps will be easy to re-install. I wouldn't worry about that unless she has some problem. Probably very easy.
Would it also work in the rest of the EU as she continues to travel?
Probably. The EU has done away with most roaming fees especially for data between EU countries. So if she buys a French SIM card and travels to Italy, she'll have a French phone number but her data should still work in Italy or elsewhere in the EU, for no extra fees. She can buy a prepaid SIM with a plan probably good for 30 days, with a certain amount of calling minutes. The plans vary. I don't know how many calls she actually makes with her phone. Most younger people seem to care mostly about data. They know how to make VOIP calls with Skype, WhatsApp, etc. and don't really need the calling minutes per se.
One tricky thing about buying a prepaid SIM in say France: she may get say 30 days of service, but she may have no way to renew it once she leaves France. (This is called "topping up".) How she can "top up" (add credit to the SIM, get more service for another 30 days) varies between each different provider. It may turn out to be easier for her to buy another SIM in the next country she's in after the first 30 days of service ends.
I suspect, if she has European friends, that they know all about this kind of stuff and can help her. The thing they can't help her with is getting her Sprint number back.
Good luck!