So first of all, I think you’re going to have a very, very difficult and disappointing time whenever you say “I want to play character X in RPG Y that has no relation to X’s own setting.” See our Q&A on playing Gandalf in D&D 3.5e, particularly the top two very-highly-rated answers that basically say “you can’t, Gandalf isn’t from D&D, instead you have to play a Gandalf-inspired D&D character.” Likewise, ultimately, this player cannot play Brigitte in Pathfinder; the character can at best be a Brigitte-inspired Pathfinder character. The best way to handle this is to take the character of Brigitte, her personality and preferences, and try to imagine how she would have developed as a character if she’d grown up in the world of your Pathfinder campaign instead of the world of Overwatch.
That said, you probably still want some kind of massive-reach weapon for her. Here are some thoughts:
Spiked Chain—not unless you port the 3.5e version
Unfortunately, Paizo notoriously, unreasonably, nerfed the spiked chain from D&D 3.5e. It no longer has reach. That makes it worthless for this purpose—or any other. Unfortunately, Paizo’s position is that exotic weapons should not be any better than martial weapons—players should just pay a feat to be special. They’re wrong, it’s a terrible position, and I wholeheartedly recommend using the D&D 3.5e spiked chain—in general, not just for this character—but for completeness’s sake, we’ll ignore that.
Scorpion Whip, or regular Whip—not remotely worth it but might work
Paizo did publish the scorpion whip, which has 10-ft. reach and is light, which is nice-ish. Not worth the Exotic Weapon Proficiency feat, but maybe that’s a price the player is willing to play. Paizo also published a number of whip-related feats—after burning three or four feats, the whip can be almost as good as a martial weapon (⌐.⌐). In both cases, presumably this player would ask for a homebrewed bludgeoning-damage version, which is no big deal. The scorpion whip is light, and whips can be finessed despite being one-handed.
Flickmace—sounds like exactly the thing, but no finesse
On the other hand, there is something called a “flickmace” which is one-handed, has the reach and trip properties, and already deals bludgeoning damage. Flickmace certainly sounds like the thing you have in those images. The only thing it’s missing is usage with Weapon Finesse. For this paladin, who already exists, already has high Dexterity, and already has Weapon Finesse, that’s a deal-breaker. But consider allowing it to use Weapon Finesse; it’s not as though there aren’t comparable weapons (such as the scorpion whip) that work with it.
For a new character, options may be better
The high-Dexterity paladin here somewhat limits your options. Paladin doesn’t get relevant features here, like bonus feats, ways to extend his reach or improve his attacks of opportunity, and so on. Really, a paladin should probably focus mostly on damage—that’s what they’re good at. And while high Dexterity is really good, it’s really good for characters who can make a lot of use of it, like archers (which a paladin can totally be) or unchained rogues. And high Dexterity certainly seems awkward considering Brigitte’s heavy armor and shield.
For a new character, though, maybe this isn’t that big a deal. A new character could be an unchained rogue, or since Brigitte is wearing pretty heavy armor, take advantage of options that don’t need Dexterity so much.
High guardian fighter—probably closest to Overwatch
A high guardian fighter doesn’t use Dexterity for attacks of opportunity, greatly reducing the importance of Dexterity for such a character.
So the closest representation of Brigitte in Pathfinder is probably a heavily armored high guardian fighter with a heavy shield and a flickmace. For a paladin who already has high Dexterity and Weapon Finesse, houseruling the flickmace to allow Weapon Finesse, or a version of the scorpion whip that deals bludgeoning damage, are probably the best solutions.
Magus with long arm and line of sand—different, but much superior
Ultimately Brigitte does a number of things that aren’t very effective in Pathfinder. Pathfinder rewards having both hands on your weapon really heavily. Pathfinder doesn’t reward shields very much at all. Pathfinder rewards high-Dexterity characters pretty well. Pathfinder doesn’t reward heavily-armored characters nearly as well. And combat maneuver math is such that it is very difficult to succeed on combat manuevers one you get into the mid levels of the game; they are not nearly as reliable as they should be. On top of that, the overriding concern with Pathfinder—that magic dominates absolutely everything—has to be considered. All told, this player may want to imagine Brigitte responding to the realities of the world she lives and choosing other means for accomplishing her goals.
If we start thinking more outside the box, being able to cast long arm becomes pretty appropriate. Line in the sand can also replace high guardian pretty well. Brigitte isn’t magical, but she isn’t from a world of high magic—and Pathfinder is a world of very, very, very high magic. Unfortunately, the longarm bracers cruelly add a near-crippling −4 penalty on attacks, and the Lunge feat and related feats are near-useless since they apply only on your turn. So casting these spells yourself becomes very desirable. And I note that both are magus spells...
Therefore, really, my top suggestion for Brigitte is not a high guardian fighter with a flickmace and a heavy shield, even though that will give the closest rendition of her. I think a magus, who makes good use of long arm and line in the sand, works better. Maybe toss in the flickmace, though she’ll need to keep the other hand free for spellcasting (remember to grab the flickmace when attacking!). Also, it seems to me that a warpriest might be even better than a magus here—if only that class could get those spells... and those tricks could be used by a paladin too, though the limitations of paladin spellcasting make that really problematic.
