Cable Incognito is OK here
Your cooktop circuit was wired using what is known as type SE, style U (or just SEU) cable. This is a jacketed cable with two insulated wires and what is known as a concentric neutral formed by the bare strands wrapped around the inner conductors and then covered by the jacketing. It is suitable for indoor applications as per NEC 338.10(B)(2) and (B)(4). (This is unlike the similar-sounding but not quite related type USE cable, which is a direct-bury rated, jacketed or unjacketed multiplex cable that cannot be used indoors as its insulation is not required to be flame retardant.)
As there is only a main panel involved (no subpanels), and both of the current production Frigidaire Gallery cooktops are 240/208VAC only units, you can strip back some of the SEU cable's jacket, twist all the strands into a bundle after peeling them away from the wires inside, feed it into the junction box with an appropriate cable clamp for strain relief while making sure the jacket is clamped with at least 1/4" of it inside the box and clamp, and then cut and strip the inside wires + cut off the excess bundle length.
From there, use Al9Cu listed split bolts or another type of connector (such as a screw type lug) listed for 90degC operation and copper to aluminum connections with 10AWG copper and 8AWG or larger aluminum to make the connection, along with antioxidant compound. With split bolts, you'll need to insulate the connections yourself as well -- this is done with a self-adhering elastomeric tape first, followed by an overwrap of ordinary PVC electrical tape.
Electrically, what you're doing here is using the concentric conductor to the main panel as an equipment ground as per 338.10(B)(2) with the two inner conductors as the hots as your cooktop has no use for a neutral wire.