It would certainly increase the PC's power. How much depends on the DM
Speak With Animals is a level-1 spell, so you would be turning an ability that normally would cost resources (or a 10-minute casting time as a ritual) and only lasts for 10 minutes into an always-on ability, which is in general extremely powerful.
user18327's response above is flavorful, but it doesn't seem to be backed up by the rules. The text of the spell Speak With Animals gives hints to its power level:
...at minimum, beasts can give you information about nearby locations and monsters, including whatever they can perceive or have perceived within the past day
So if you're ruling Speak With Animals as the book spells it out, then the PC with this always-on ability would essentially be able to have almost unlimited instantaneous knowledge of any area that has animals. Animals won't deny the PC the ability to speak with them, and they seem to always tell the truth at least as far as they are able, so RAW you don't have to worry about things like personality or lack of intelligence (at least as far as scouting is concerned, which is what I assume most people will use this for).
In a vast desert with no wildlife this probably won't really be much help. In a dense forest you probably won't be able to swing your arms without hitting something that can tell you about its surroundings.
As far as it being overpowered, that is an opinion, and it depends a lot on how you decide it works and what overpowered means to you. Making it a passive, always-on ability without any caveats, and assuming it works exactly like the spell in the book, then it would most likely be an extremely powerful feature that at least one PC in your party would feel obligated to take. If you as the DM modify it and make changes then obviously its power level would go up/down. If you're looking for a way to give a character flavor without increasing their power level, then giving them an always-on 1st-level spell is probably going to be difficult to balance.