Does it have a removable battery? If so, it's worth pulling it out for a few minutes. Probably won't help, but there's a chance and no downside.
Otherwise, it sounds like your only options are:
1) full factory reset (which will erase everything)
2) contact Alcatel, or your carrier if you bought through them, and tell them that their update broke your phone so it's their job to fix it. They'll still wipe the phone in the process of fixing it though, so you've nothing to lose by trying the factory reset.
That is unless you've rooted it or otherwise modified your system software, in which case actually the truth would be that you broke it by accepting an over the air update on a modified phone. If that's the case it's probably best to find out how to reflash the phone to stock yourself before bothering the manufacturer, though that's still the final option if you can't fix it.
(Edit: or, as SavageRobot says, if you are rooted and have a custom recovery then flashing a new ROM, or restoring the backup if you have one, is also an option).
If you've not modified it then reflashing to stock yourself - however that is done on an Alcatel - is also an option. But if their update broke an unmodified phone I kinda think they should be told about it and should take responsibility. Note that if you bought it through the carrier and they customised the software then the update came from them, rather than directly from Alcatel, which is why who you should contact could depend on who you bought it from.
