The overall demographics of modern Forgotten Realms, ie. say the last couple centuries, seem not to have changed much over the various editions of the game. Since around -3000DR, when the human archmage Iolaum raised the first enclave of what would become the Netherese Empire, humans have been increasing in influence, while the dwarven and elven empires have declined ("Age of Humanity").
For individual cities, detailed statistics are available in Forgotten Realms Adventures (2e) and Forgotten Realms Campaign Setting (3e FRCS). Certain locations, like Evermeet or Luiren, are exclusively or mostly non-human (elves and halflings respectively); others are mentioned to have significant non-human populations like Lantan (gnomes). However most of the settlements on the surface of the continent of Faerun are predominantly human. You can get some of these data (even exact percentages) on the FR wiki.
If you are interested not in particular locations, but in the overall percentage, we can say that humans are the dominant species. In order to get data about the whole planet altogether, it would be meaningful to refer to a sourcebook that considers the whole planet as a unit, as it is observed literally from space: In the 2e game accessory Realmspace, the population analysis is summarized (page 18) as follows: "Human and humanoid races most prevalent".
Finally on the RPGnet forums, a poster with the nickname Handigar claims to have added up all the data from FRCS. Quoting from that post:
- Faerun's total sentient population is about 66 million, roughly comparable to modern Britain or the Roman Empire.
- Humans are the most common race, at over 80%.
- After humans, halflings are most common with 3.5 million, followed closely by Dwarves. Elves and Orcs are rare outside their concentrations.