France is a big place. Do mean just over the border from Geneva in the Alps, or do you mean Alsace which is just over the border from Basel and southwest Germany? Or do you mean Paris or Normandy?
If you do wind up with an intercountry pass - unneeded and overly expensive and cumbersome in my opinion, but please answer Where? above, it isn't called a eurorail pass. You may have conflated two distinct words, Euro, the common currency in many European countries, and rail for train. The name of the pass which was named long before the EU - European Union and its currency the Euro, back when we just spoke about Europe. It was 3 words stuck together - Eur (Europe) rail (train) pass (pass) - they left out the double r and it has been called Eurailpass ever since.
In some circumstances - few but some - it may be worth the high cost, but probably the three countries where it is least helpful are Italy, Switzerland and France.
Italy because regular train fares are so darned cheap and so easy to get, and because to go on anything other than the very slowest trains you have to pay extra - around 10€ (10 Euros) for each person for every leg, if you have to change trains you pay twice - in addition to your pass. Some normal long distance fares are as low as 10 or 20€. So you save nothing and pay more. There is an entire network of high speed trains run by a competitor (Italo) who don't honour the pass at all.
Switzerland because the Eurailpass discount on the mountain cable cars and trains and gondolas is much less than various of the Swiss solutions so you are spending a lot of money to not get the best deal.
France because, like italy, you have to pay extra for faster trains, and often the TGV is the only reasonable answer, and quotas restrict the number of seats available to passholders on international trains. And other really cheap deals are available.