Maybe.
Using a sword as a spell foci is a house ruling by your DM and so the answer to this question ultimately falls to him/her, but to try and get as close to RAW as possible...
If the sword is your holy symbol, then it can be used as your spell foci. PHB 151:
[...] A cleric or paladin can use a holy symbol as a spellcasting focus [...]
There is no entry in the DMG for +X generic spell foci, staffs, or wands (see relevant question here). The closest entry I can find along these lines is Wand of the War Mage (DMG 212) which states:
Wand, uncommon (+1), rare (+2), or very rare (+3)
(requires attunement by a spellcaster)
While holding this wand, you gain a bonus to spell attack rolls determined by the wand's rarity. In addition, you ignore half cover when making a spell attack.
So there is at least a precedent for +X spell foci granting +X to attack rolls.
You DM would likely rule that you get +X to attack rolls for spells once you are level 2 (which is when a Paladin receives spellcaster status). Or they might rule that you have to acquire a separate +X holy symbol to get +X to attack rolls for spells (though this would make less sense in my opinion).
Would it be broken for you to get +X to attack rolls? I wouldn't say so, though it's very convenient for you. It's the same statistical advantage as having a +1 sword and a +1 holy symbol (necklace), but without the time/effort of acquiring two magical items (which isn't trivial). Any bonuses beyond the attack roll and I'd say it's giving too much. I would want a Wizard PC with a Wand of the War Mage to at least think 'my spells get to ignore half cover, yours don't' when comparing their wand to your sword (don't laugh, don't laugh, don't laugh...)