Can a character under the effects of a confusion spell make saving throws? I.e. if I'm confused can I dodge a fireball?
If a spell forces a character or target to make a Saving Throw, then they make that saving throw.
The Confusion Spell specifically states that the target cannot take Reactions, but a Saving Throw is not a Reaction, it's instinctive.
The difference between a Saving Throw and a Reaction is that you make a Saving Throw any time an effect or spell calls for it unless a Condition such as Stunned would prevent you from making that Throw, while you only get one Reaction per Round which you choose when to use.
Reactions include (but are not limited to) Uncanny Dodge (Rogue Ability) and Attack of Opportunity.
It is worth noting that there is also a Dodge Action (not Reaction) which sacrifices your turn to give you advantage on Dexterity Saving Throws and imposes Disadvantage on all Attack Rolls from sources you can see. This could be prevented by Confusion, but only if the creature rolled low-enough on the D10 roll.
Here's the description of the Confusion spell:
This spell assaults and twists creatures' minds, spawning delusions and provoking uncontrolled actions. Each creature in a 10-foot-radius Sphere centered on a point you choose within range must succeed on a Wisdom saving throw when you cast this spell or be affected by it.
An affected target can't take reactions and must roll a d10 at the start of each of its turns to determine its behavior for that turn.
1: The creature uses all its Movement to move in a random direction. To determine the direction, roll a d8 and assign a direction to each die face. The creature doesn't take an action this turn.
2-6: The creature doesn't move or take actions this turn.
7-8: The creature uses its action to make a melee Attack against a randomly determined creature within its reach. If there is no creature within its reach, the creature does nothing this turn.
9-10: The creature can act and move normally.
At the end of its turns, an affected target can make a Wisdom saving throw. If it succeeds, this effect ends for that target.
At Higher Levels: When you cast this spell using a spell slot of 5th level or higher, the radius of the Sphere increases by 5 feet for each slot above 4th.
No part of the description prevents the affected creature from making saving throws (in fact, they kind of need to be able to make saving throws in order to end the effect of the spell on them before a minute passes).