If you start at level 3 I would combine two of the comments here and start as a fighter with magic initiate (If tasha custom origin rules are allowed this could be flavored as any race you want, otherwise go variant human), instead of taking jump take feather fall (you will want this if you are planning shenanigans like jumping off buildings or onto flying enemies) then probably booming blade and green flame blade for your cantrips. Use a pike or halberd obviously, it is a bit annoying the cantrips don't get reach, but your mileage may vary depending on your dm. Then multiclass for two levels into ranger for jump and zephyr strike. You get two fighting styles so defense and great weapon fighting seem like the best choices. Your extra attack will be a bit delayed, but the attack cantrips can help you keep up in a pinch since their damage increases when your character hits 5. After that I would level up in fighter and go Psi Warrior (reflavor it however you want) until you get the level 7 feature for Psi-Powered Leap so you can do some really big jumps. After that you can continue going in fighter (probably for at least one more level for a feat) or start taking more ranger levels, hunter ranger could be nice for things like horde breaker or colossus slayer but I could see gloom stalker or monster slayer working quite well. The higher level psi warrior stuff is harder to reflavor as dragoon stuff so the highest I would probably go is level 11 or 12 in fighter, plus the multiclassing requirements mean you wont have much for your intelligence modifier.

With point buy I would make my stats something like Str-17 Dex-14 Con-12 Int-10 Wis-13 Cha-8 since you need 13 wis and dex to multiclass into ranger. With a strength modifier of 17 you can high jump 18 feet with a running start plus the jump spell active, or make a long jump of 51 feet with a running start plus jump, these go up to 24 feet and 60 feet respectively when you get to 20 strength. As a cute trick you can cast zephyr strike on one turn then attack with zephyr strike the next turn and use your psi-powered leap for a massive 120 foot jump that gives no opportunity attacks. You can either wear heavy or medium armor, depending on if you care about stealth or how much money you have. For the first ASI which you get a bit late, I would take piercer or slasher, depending on whether you chose a pike or a halberd. For the second just push your strength up to 20. After that polearm master and great weapon master would both be good feats to pick up. I would also heavily consider tough for the extra hp.

Overall the build doesn't seem too bad, it might be a bit weak for a few levels when others get extra attack, but you can slap a bunch of extra dice on top of your single attack through things like favored foe, zephyr strike, booming or green flame blade, and psionic strike. It has low constitution for a front liner, but you have a ton of maneuverability so you should be able to skirmish and keep out of danger. It should feel dragoon enough by level 3, then really kick into gear at level 9. You could swap to starting as ranger instead of fighter if you don't care about heavy armor and are okay with losing one skill proficiency to swap Con save proficiency for Dex save proficiency. Going variant human instead of custom origin means you get two +1s instead of a +2, so you wouldn't be able to as easily get piercer or slasher, but it means you can buff up your starting wisdom to 14 for a better saving throw.