Can you blanch French green beans the night before you cook them, and store them in the refrigerator?

Cynthia is absolutely correct - I do this all the time.

For me, 5 minutes is a long time. Depending on the amount in the batch I would suggest tasting a piece after 1 minute, then in 30 second intervals.
No point going to all that work to get limp over cooked beans.

You betcha! We did this at work too.

Absolutely! In fact, teach people to blanch a big batch of them when they get them home from the store. That way, they're always ready for something - a salad, or to be finished off as part of dinner. Plunge them into boiling water for 5 minutes, them lift them immediately into an ice water bath. Let cool completely, then drain and refrigerate.