Yes, framing a print or painting can add to the overall value. Sometimes frames are worth more than the prints or paintings themselves!
If it was your grandma's and you love it, then it has a high sentimental value for you. As such, there really isn't a monetary amount of value that could be placed on it for you. It is priceless! I have many such objects in my home that are not worth very much in monetary terms, but are priceless to my children and I because of them being handed down as part of the family.
I will give you another example of what I am describing. Part of what I do for a living is that I am a piano tuner/technician. Over the past almost two years, I have been doing a great amount of work on a customer's old upright piano that had belonged to his grandmother. He is paying me over $3,000 to do the work that I am doing. However, this piano will never be worth more than $300 or $400. Is it worth it? He thinks so. It is a nice tribute to his grandmother to have her piano brought back to much the way that it was when it was new, nearly a hundred years ago.
Sorry about my rambling, but I just wanted to put things in perspective.
If your etching is what I think that it is, that being a print that is from the Paris Etching Society, then it is not likely to be worth much money.
However, you did say "original." Are you certain that it is an original?
I did the following search
Lucien Dasselborne original - Google Search There is some information on some of the sites that may be helpful to you. Just by what I have found, even if it is an original, it may not be worth more than about $50.00. But, the frame might make it worth even more than that.