Seven inches? That isn't a new plant, that's simply an extension of the old one. There can't be much root on it, and you can probably barely get a shovel in there to cut it off.

When they come up a couple of feet away, then you make plans to relocate them.

Hmm, maybe I need to take a picture then, maybe then it would be clearer. I surely don't want to split anything up if I don't have to. That would be tragic.

Max...I've had good luck removing suckers from several different roses, including Roseriae d'l'Hay. I just get down, try digging under the sucker with a hand trowel or my hand to see if it has roots forming. If so, I use secateurs to cut it off the main rose and dig it up. You could see if it has roots forming, then cut it from the main rose and let it grow in situ on its own for a while as well.

A little bit of tid ...my suckers of this rose have gotten crown gall, but it didn't seem to affect the main plant.

Robert

Is your Roseraie own root?
If so, you can propagate it by digging up a length of root (bigger diameter the better), cutting root into 3-4 inch long pieces, and planting the pieces. Top growth comes up quickly (1-2 weeks).