A better question to ask is "Will taking the train save me any money?"
And the answer is yes and no...
Taking the train in Alsace will save some people money and others not.
It depends on where you will be going and how often you will be traveling.
It also depends on how many people will be traveling with you.
If you check the prices for a rental car in Alsace, you'll find that they tend to run between 400 euros and 600 euros for a week (in my personal experience).
If you take the total cost for renting a car in Alsace and divide it by the number of people traveling with you and then divide it by the number of days you will be in Alsace, you will get a per day per person travel cost.
If that number is under 20 euros, it may be cheaper to rent a car.
But it also depends on how much traveling you plan to do.
If you plan on making at least three or more trips per day, you may find renting a car in Alsace is cheaper.
And if those trips that you are planning are more than 45 minutes from your starting place, renting a car may be less expensive.
Regardless of the costs, there are more advantages to renting a car in Alsace because you will have access to more villages and attractions.
You will be free to do as you please when you are driving in Alsace too.
With the trains, you have to keep track of train schedules and trains generally run once an hour.
But with the trains, you also don't have to worry about drinking and driving after one too many wine tastings.
Personally I prefer to drive in Alsace because my favorite places to go don't usually have train stations (and I don't mind spitting while wine tasting on the wine road).
I hope that helps you with your Alsace travel plans...