Probably between CR 9 and 14 depending on how clever your Hydra is - assuming you bring the save DC to 16, more in line with expectations.
The Hydra is a tricky beast to figure out balance for, due to its unreliable number of heads. However, if we look at the stats compared to the table, it seems that at least the base stats (ignoring the Multiple Heads mechanic) line up decently with a normal creature for its CR-1.
That is; you'd expect a balanced offense/defense CR 7 creature to have about AC 15, slightly under 175hp and deal about 50 points of damage with a +6 attack bonus. The attack bonus on a Hydra is slightly higher, but everything else lines up; so by that reasoning you can reasonably ignore its Multiple Heads mechanic when determining base CR and then bump its CR by 1 for having it.
Based on that logic, it's still hard to factor in your new attack, mostly because of the very low save DC. A DC 12 is lower than even the recommended DC for a CR 0 creature, which is so far below what the CR 8 of a regular Hydra that it's hard to compensate for.
If we bump the DC to the more reasonable DC 16 (which happens to line up nicely with 8 + prof + con mod for the Hydra) that matches roughly with its normal +8 attack bonus (both being the expected level for CR 8; or slightly above the CR 7 the other stats seem to line up with) then we can run some calculations.
Your attack deals 14 damage compared to the Hydra's normal 10, a clear increase. It's also a Cone, meaning you could potentially hit multiple characters with it; a 30ft Cone is pretty big.
The true challenge will depend heavily on how many characters you'll hit on average when using a breath weapon.
If this Hydra is smart or cunning (most aren't, but I don't know yours) then it could expect to easily hit 2 characters with each breath; that means it'll be able to bump its damage to 140 in the first round (5 breaths x 2 targets x 14 damage) and then be able to add extra breath attacks and bites for 106 damage over the next 2 rounds (roughly 2 breaths recharging x 2 targets x 14 damage + 3 bites x 10 damage).
That means an average of about 117 damage; bumping its offensive CR up to 19. If we average this with its defensive CR of 7, you'll end up with a CR 13 creature, or a CR 14 one if we add +1 CR for the Multiple Heads ability.
This will be one mean monstrosity, but also a major glass cannon compared to the original.
If you play the creature really dumb, and only target 1 character in each breath, your CR will come out closer to 70 (5x14) on the first round and around 58 (2x14+3x10) on the other rounds, which averages to 62. That's closer to CR 9, which averages to CR 8, which if we add +1 CR for the Multiple Heads ability means we'll end up at total CR 9.
That's nasty, but not a lot stronger. Keep in mind this is with bumping the save DC to a more respectable 16. I'm not sure how to account for a really low save DC here, it will probably prevent a lot of damage and make it quite a bit weaker, but I'm not sure by how much.
So if your Hydra spams breath weapons around in a way that each hits about one person, it'll be slightly tougher than a normal one, but not much so. If it is clever about targeting as many people as it can, it will probably wipe the floor with a party challenged by a normal Hydra.