In 1.0 Minfilia specifically stated that the Echo really did grant the player 'mastery over all languages of Eorzea' - as far as this went she stated she believed that this was actually a side-effect in itself from 'touching a person's soul', by intergrating themselves into another's thoughts and memories, the Echo allowed that person to subtly understand them, even if they only speak another language previously unfamiliar to them. Although it would make sense to be instantly granted the ability to understand one unknown language by using the Echo on one person, it seems that just one use is all it takes to understand all of them, including beastman languages (see next paragraph).
It's not stated outright but given the fact there is a standardized written Eorzean alphabet used by all nations in Eorzea, it stands to reason that would also apply to spoken language as well, hence it seems that all the nations of Eorzea speak the same language. It's unclear, but it's also possible that the Garleans speak the same langauge, or at least a varied dialect of it, as you never hear them speak anything different.
In fact, in 1.0 it was made quite clear the Echo's language mastery was not so much for understanding another member of the five races, but more understanding beastmen races - the beginning of the original Gridania storyline the fact the player could understand mooglespeak was in itself a hint that something very strange was going on, as npcs remarked that mooglespeak was a frustratingly difficult language to master, and for an apparent outsider who just showed up out of the blue to speak it like the common tongue, was naturally regarded as an amazing thing (besides the player, Yda and Papalymo were also clearly shown to at least understand mooglespeak, when a moogle mistakenly believed they wouldn't understand the insult he made at them, which an irate Papalymo soon made quite clear he very much did, leading a bemused E-Sumi Yan to offer a strained apology.
As well, during the first quest for the Path of the Twelve in 1.0, Minfilia clearly demonstrated her lack of this aspect of the Echo when a party of desperate sylphs occupied the Waking Sands desperate for help from the organization, and because she couldn't understand what they were saying (in fact, Tataru actually admitted it seemed no one then in the Waking Sands could), an exasperated Minfilia desperately called out for another member to translate what they were saying (the player ends up doing this when they eventually show up in her office).
It's somewhat ironic then that in ARR the only language that the player doesn't seem to be able to understand is the language of the Ascians, as all we hear when they speak is an unintelligible croaking mass of random syllables, but is translated in red text (this led Lahabreha to sarcastically quip that he had to speak to the player in "their crude tongue" when he realized that the player didn't understand him). I guess even the Echo has a limit.).
Ironically enough, originally in 1.0 the Garleans actually regarded anyone with the Echo as a heretic for this very reason - because they could understand the beastmen languages, they were basically regarding anyone who communicated with the beastmen as a beastman themselves (they stated this as propaganda from linkpearls dropped from Imperial airships, calling on the citystates to accept Imperial rule and aid the Empire in the extermination of the beast tribes). Accordingly Minfilia at this time entertained notions of actually joining forces with the beastmen against the Empire, thinking that at the very least being able to communicate with the beastmen would allow them to come to a mutual understanding with the beastmen, and such a union would be better than both societies trying to face the Empire alone (it must be noted that this part of the storyline was Tanaka-era and preceded the decision by the development team to bring down Dalamud - accordingly the Grand Companies didn't exist at this point).
It was also before it was known the beastmen had actually begun to summon - the citystates knew the beastmen had stopped the trade in crystals they formerly had with the citystates and that they were conducting strange rites, but until the player's Path Companion went behind Minfilia's back and, with t he player, saw first-hand the very first summoning of Ifrit by the amalj'aa, allying with the beastmen was considered the best option available. As well, the Garleans didn't actually know that the Echo protected a person from being influenced by a Primal - once they realized this they changed tack and became hellbent on trying to understand it, somewhat ironic considering their previous attitudes towards it.
In any event, it was definitely clear that Tanaka had been planning the Echo to be something far bigger than what it actually turned out to be in ARR - a shame as the concept is very interesting and could have been used to have taken the storyline in many directions. But I guess we'll have to wait and see if Yoshi-P has similar plans for it, which I hope he does.