Is the JSM also an option for helicopters?
It's planned, as is a VLS and submarine launched variety, but unlike NSM, JSM is still in the process of being refined and has yet to reach a service stage. F-35 and P-8A integration are the priorities right now since both of those are seeing widespread proliferation among likely or current F-35 users (and there's a push to limit the Turkish SOM-J's spread among NATO partners), and that Norway itself is buying both types. Following that are going to be subsurface variants to arm Norwegian submarines, and possibly those of Germany, Poland, the US, Japan and Australia, all of whom have purchased or intend to purchase JSM (and are themselves NSM users). Only after, unless Raytheon decides to expedite the process, will work an a helicopter launched JSM commence.
It's currently a low priority.
I think the Marte is Italian. Anyway, the US will push for their own wares on India over European. And the MH-60 will likely win the tender for 123 helicopters anyway. So whatever the USN operates, India will operate when it comes to the MH-60.
Matre's design is Italian, but the missiles IP is owned by MBDA, which is French (not a consortium, but a collaboration between several transnational contractors). Developmental work on the Matre ER is being done primarily by Italy for use on their Typhoon and NH90s though.
As for the US, their helicopters aren't used for anti-shipping generally, but for small boat interdiction or assault. They carry Penguin which is capable of sinking ships, but is generally considered rated for frigate sized boats unless using multiple missiles, and Hellfire, which is targeted as a solution against swarm boats or fast attack craft. Apart from those two Maverick is the only other helicopter capable anti-ship missile in the US inventory and can be, but isn't operationally, carried by the AH-64 and AH-1. Operationally Maverick is only used in a maritime role by American P-3s.
So India's options if they're intent on using (or are forced to) American helicopter launched anti-ship weapons are limited to Penguin, being phased out, Hellfire, likely already on India's order list, Maverick, by only for naval attack helicopters and MPAs or hoping the US either allows India to integrate another weapon or hope they move forward with a helicopter launched JSM/NSM rather quickly.
At present the US doesn't have plans to go forward with any armament outside of Hellfire since in its experience helicopter engagements against ships take place at extremely limited range which puts the necessity of a Penguin or JSM outside of their necessity versus a Royal Navy or Italian Navy who's lack of alternative maritime strike elements necessitates the use of supplementary weapons like Matre ER, Exocet or Sea Venom.