I don't believe Picard's exact height has ever been specified in any of the TV episodes or movies, but I think we can safely conclude that neither he, nor other humans from his era, are especially tall compared to humans from ours, based on various instances where characters from the 22nd-24th centuries have interacted with those from the 19th-21st centuries.
Notably, Picard himself appeared somewhat shorter than Mark Twain, whose height in real life is listed as approximately 1.74 metres (though the actor playing him may well have been taller).
Also, if you're rounding to the nearest metre, then the vast majority of people today (including Patrick Stewart) can be described as being "about two metres tall", since that would encompass anyone between roughly 4'11" and 8'2" in height.