New SNCF discount cards

Yes they can. They can even be bought on the self service kiosks (borne libre service) that are dotted around major stations and in towns too. You need a chip and pin Visa or Mastercard to operate the kiosks but it's so much better than braving the queues at mainline stations.
You need a passport photo.

Ginger, are you talking about cards like the Senior Advantage card from SNCF? I bought mine at a ticket window at the first train station I visited. Contrary to the previous post, I did not need a passport photo (I did need to show ID as proof of age, though).

I used my US chip-and-signature credit card in many SNCF ticket-vending machines earlier this summer. Only once was there an issue, most likely due to connection problens to the card network. I did not buy the card itself from a vending machine, however.

Don't forget to have your passport available as proof of age when you buy the card. Then present the S.A.C. when buying a discount ticket at a staffed counter. Also expect to be asked for the Senior Advantage Card on the train when the ticket inspector comes along.