Can a wizard 1/ fighter x cast multiple spells per turn, because of the extra attack feature?
No.
But if you mean, because of Action Surge, then yes.
Action surge makes sense, I was just curious if a wiz/fighter could get up to casting three or four spells per round. Would have been a terrifying nova.
That is ruled out by the fact that Extra Attack grants attacks , when you take the Attack action.
When you cast a spell you take the Cast a Spell action.
Some spells require you to to an attack, but that's still part of a Cast a Spell, action.
I suppose it might happen tho, to encounter a spell that after you've cast it (presumably by Cast a Spell action) will let you do some magical attacks using the Attack action for the duration of that spell. In such case, you would indeed get multiple attacks if you have Extra Attack. (Example: this is what would happen with Produce Flame, if only such spell didn't have a special clause saying that if you attack with the flame, the spell immediately ends)

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.