[RPG] Which class should the “fallen” paladin change to

If you want to give your fighter more access to magic without rebuilding you're going to be limited to skills, feats, and magical items. None of these will give your fighter heavy magical abilities, instead letting you play the character as someone who has learned basic magic.

Skills
The skills that increase magical knowledge are:

Knowledge (Arcana) - represents general knowledge your fighter has acquired about magic; what an arcane symbol means, how the local mage guild heirarchy is organized. Stuff he would learn in school or from talking to spellcasters.

Spellcraft - much more specialized knowledge about specific magical effets. While Knowledge (Arcana) is theoretical studies, this is applied studies. Being able to recognize magical effects, figure out what spells are being cast. Knowledge gained by seeing magic in action, how it's been used.

Use Magic Device - knowing how to use the magical items that are common to spellcasters; staff, wands, scrolls, etc. The Evil Necromancer has defeated the parties fighter and is now monologuing to the rest of the party about their imminent defeat. The tired fighter rolls over, grabs the wand of fireballs from the necromancers belt and make a brilliant quip as fire blossoms around them.

Feats
There aren't a lot of feats that contribute to magical abilities. The first one I recommend is Able Learner from Races of Destiny. This feat treats all skills as being in-class skills. This will allow you to level up the above skills quicker.

The other feat that is useful is Magical Training, from the Players Guide to Faerun. It allows your character to cast three 0-level arcane spells per day as either a wizard or sorcerer.

Items
Have your character carry around magical items that are commonly associated with spellcasters. Staves, scrolls, wands. Combined with Use Magic Device this allows the fighter to have access to magical abilities.

A staff is an excellent choice of a magical item for this type of fighter. They can use it as their melee weapon, and use the magical abilities within it. A great surprise tactic when fighting: thrust, thrust, parry, Cone of Cold.

According to the list of Alternative Class Features, there are two ACFs for the Paladin which replace Spellcasting. Furthermore, this answer by JohnP features a feat that fits what you want.

• The Holy Warrior ACF from Complete Champion (p.49) grants bonus feats from a fixed list at 4th, 8th, 11th and 14th level. The list includes some basic combat feats, mounted combat feats, some turning and all [Divine] feats.

• The Paladin without Spellcasting Variant class from Complete Warrior (p.13) grants the paladin some supernatural abilities, such as making every weapon be Good-aligned, or a 1 minute/lvl untyped +4 Bonus to Strength.

• The feat Lost Traditions from the 3rd party book Bastards and Bloodlines allows you to change your casting stat for any one spellcasting class to any ability, including Strength or Constitution. While potentially very powerful, allowing this feat for this particular case should not produce too many problems, as Paladins do suffer from MADness and their spellcasting is a tertiary ability at best.

Of these three options, I'd personally lean towards Lost Traditions. Most of the Good [Divine] Feats require Charisma, which your Paladin doesn't have, and the spell-less variant is a bit lackluster in general. Seeing that you want to distance the Paladin player from the Fighter, letting him keep his spellcasting is the best way, as it allows for unique effects the fighter doesn't have access to.