The Franklin-A is an Uncommon Grade 4 Explorer, and you get it by scrapping your existing Franklin rather than building it from scratch. Scrapping rewards Franklin Advanced Data Cores, and the amount scales steeply with your Franklin's level: 200 cores at level 41-45, 150 at 36-40, 50 at 31-35, 25 at 26-30, and nothing below level 26 -- so it pays to level your Franklin as high as you can before scrapping it. A maxed Franklin hands you enough cores for a full set of Franklin-A blueprints in one go. The Franklin-A keeps the same job as its predecessor, dealing vastly increased damage to Swarm targets, just with a higher ceiling.
Franklin Advanced Data Cores convert into blueprints through the Franklin 2.0 Blueprints bundle in the Resource Refinery. Once built, the Franklin-A upgrades the same way the original Franklin does -- through materials earned from missions -- and its first Franklin-A-specific mission requires you to be above level 35.