She dies.
Look, lets change the scenario a bit. Instead of a level 6 fighter, he's a 0-level NPC.
Does that change your answer?
It doesn't for me. That 6th level fighter doesn't have an special miracles or talents he can call upon, any more so than the local dirt farmer does. He's a hero, sure, but he's not a hero powered by his god's divine magic...just his mundane faith, which in him is presumably as strong as it is in Dirt Farmer Lydia. Going to services and tithing and being devout -- these are things the Dirt Farmers do just as much if not more so than the Fighter. His extra-special worship doesn't make him any better than them.
In-character, that Fighter chose to protect his wife in their dangerous line of work by wearing heavy armor and taking blows and if he failed to do that, he failed to protect his wife, and thus, she dies. You failed. There are consequences for failure that just asking nicely won't get you out of. NG gods let devout people die all the time -- presumably even those who ARE powered by divine magic.
Out of character, the fighter's player made a choice NOT to play a healer. Presumably, not being able to heal his character's dying wife was a consequence of that choice the player was willing to live with. In battle with an orc or old in bed, sooner or later, she was going to die. As a fighter, you accept that you can't do much about that. Why would I rob him the chance to play his character as he develops into a grieving widower who perhaps questions his loyalty to a god who would allow such a thing to happen? That's a juicy character conflict, right there!
As a DM, there's things that a fantasy world can offer that become available to the fighter because of his status as a hero and his membership within the church. Perhaps a high-level cleric can take pity on the fighter and raise her from the dead (perhaps in exchange for some token service...like retrieving the lost relic from the vault of the undead?). Perhaps a necromancer offers her services, tempting the fighter down a dark path. Perhaps there is awkward sexual tension between the Fighter and the new character of the player who once played his wife! Perhaps he can go see her soul resting blissfully in the afterlife while he jaunts through there on his way to Hell to kill Asmodeus. Maybe he takes a level in Cleric to make sure this kind of thing never happens again. Heck, if this is 3e, find the nearest cleric with access to True Res, and pay him a boatload of gold, and she'll be right as rain in a night.

Either way, there is going to be an awesome funeral scene where a bunch of recurring NPC's show up to offer their condolences!
These are all the seeds of a much more interesting story than, "Turns out, worshiping a god gives you a free pass sometimes."
She dies. Characters die. Adventurers die. Being a married adventuring couple is probably signing up to be widowed in the near future -- it's a dangerous profession. If the fighter couldn't prevent this by Being A Fighter, being a fighter who is especially devout ain't gonna change that any more than being a dirt farmer who is especially devout. But what being a Fighter might let you do is access ways to bring her back that the dirt farmer doesn't get. But it ain't bring back the dead. Those sorts of prayers are like asking the gods for a pony for your birthday or for your local knight to win the joust. Even gods of goodness and light view things in bigger terms than individual lives.