The bridge was built (actually rebuilt) in 1905 in two levels, allowing the passage of the then new metro, plus cars, pedestrians, bikers… It was originally called the Passy Bridge, named after the area Passy on the right bank. It got its new name in 1948 to commemorate the battle of Bir Hakeim (Libya 1942-43).
The bridge crosses the Ile des Cygnes (the Swan Island). You can use some stairs and then take a walk all along the narrow island to its extreme south, where you can find the smaller version of the Statue of Liberty.
The statue you see is a gift from the Danish colony in France (1930) and the decorations on the side of the bridge date from its creation; symbols of the French nation are fixed to the bridge.
The bridge has "co-starred" in several films, the most famous one perhaps being the Last Tango in Paris by Bertolucci with Marlon Brando; the apartment was situated in the last corner building, just at the starting point of the bridge.
Some of the original photos can be seen on my other blog , "Peter-photos".