(covers information from several alternate timelines)
The Franklin-type was a small starship design operated by Starfleet in the mid-22nd century. After the formation of the United Federation of Planets in 2161, the Franklin-type was in the Starship-class.
The class was presumably superseded by the NX-class, the first class capable of warp five, launched in 2151. At least one Franklin-type vessel, the USS Franklin, was still in Starfleet service in 2164. (Star Trek Beyond, Star Trek: Enterprise)
At the forefront of the design that later came to be emblematic of Starfleet ships, the Franklin-type featured a saucer-shaped living and command section that contained all necessary control for ship's functions, along with living quarters. The Franklin-type had two impulse drives positioned at the aft of the ship, facing aft, on either side of a large indent in the saucer.
Positioned on two pylons, stretching back and a little outwards from the ship, were two nacelles housing the warp engines. The USS Franklin, launched in the late 2140s, was the first Human ship capable of warp 4, making it incredibly advanced for its time.
Unlike later classes of ship, the Franklin-type was built in space and never intended to land on or take off from a planet's surface. The only known way for one of these ships to launch from a planet was for it to be dropped off a cliff, causing it to reach terminal velocity, at which point the stabilizers could be initiated for liftoff.
The Franklin-type contained transporters, but they were intended for cargo use, not for living matter. However, they could be modified to work on living beings. The Franklin-type was also armed with pulsed phase cannons and spatial torpedos. (Star Trek Beyond)
The bridge was at the top center of the saucer dish, containing all essential command and control functions. The commanding officer of the ship sat in a chair at the center of the bridge, with the helmsman in front of them and communications, science, and engineering stations at consoles spread around the room. Directly in front of the helmsman was the main viewscreen, a transparent window onto which technical information could be displayed.
Directly aft of the bridge was the transporter room, which consisted of an open semicircular transporter chamber facing the entrance door, which was next to the control panel for the transporter. Controversy over transporter use at the time meant that the transporter aboard the Franklin-type was only intended to be used with cargo. However, modifying the transporter aboard one Franklin-type ship, the Franklin, in order to transport Humans, was not a significantly difficult venture. (Star Trek Beyond)
The Franklin-type had a mess hall, a warp core directly next to the claustrophobic main engineering chamber, a cargo bay, and a set of officer's quarters. The cargo bay and engineering were located on deck 3, the lowest deck. (Star Trek Beyond)
- USS Franklin (NX-326)
The Franklin-type was designed by Sean Hargreaves, who described it as initially being "almost like a large shuttlecraft." Regarding its resemblance to Doug Drexler's NX-class, Hargreaves stated that the Franklin-type was designed independent of that earlier-designed class, with the Franklin-type initially featuring nacelles in the down position before the script of Star Trek Beyond required them to be flipped above the saucer section for a launch sequence in the film.  In one of the earliest Franklin concept images that Hargreaves produced, pennants depicting the Starfleet insignia were displayed on the side of the engines. (Star Trek: The Official Starships Collection, USS Franklin Special Issue, p. 11) In hindsight, he explained that these arrowhead-style pennants were originally only placeholders that were never changed. According to the designer, the Franklin was intended to resemble a freighter and was 450 feet long.