Flanking the Seine: Answer

SPHINXES

A pair in front of the pavillion, Hôtel de Salm (now the Museum of the Legion of Honor), last quarter of the nineteenth century. 2, rue de la Légion d’Honneur. 7th arrondissement. Metro: Musée d’Orsay or Assemblée nationale

and another regal guardian at the entrance to the Tuilieries Gardens (brought to Paris in 1855). Intersection of Quai des Tuileries and the Avenue du Général-Lemonnier. 1st arrondissement. 
Metro: Tuileries 

These sphinxes, couching on either side of the River Seine, all deviate from their Egyptian prototypes in that they are clearly female. FUN FACT: In French, the word for a female sphinx is "sphinge."

A Pair of Sphinxes at the Museum of the Legion of Honor: Left Bank

Photo: Emily Reed and Becca Barton

At the back of this former palace (originally built in 1786; burned in 1871; rebuilt in 1878), two extraordinary sphinxes hold court. Like the late eighteenth-century sphinxes on the gateposts near Saint-Sulpice, these examples are shown crouched in the typical guardian pose. But unlike their stone predecessors, these sphinxes are painted cast iron. 

Photo: Mary B. Shepard

Powerful muscular lionesses with impassive classicizing faces, these "sphinges" sport long braids, floral breastplates, and abundant laurel wreathes. Note the contrast of the lion's body bristling with energy and the languid tail draped over her back. 

Photo: Mary B. Shepard

"The Sphinx of the Tuileries": Right Bank

Phillip and Maura spotted this majestic "sphinge" across the river Seine: it guards the Tuileries Gardens at the riverside entrance at the intersection of the Quai des Tuileries and the Avenue du Général-Lemonnier.

Photo: Phillip Townsend and Maura Gleeson

She is actually not French in origin, but from Sevastopol (formerly Sebastopol) in the present Ukraine--having been brought (originally one of a pair) to Paris in 1855 as booty during the Crimean War.

Photo: Phillip Townsend and Maura Gleeson

In his poem, "The Sphinx of the Tuileries" (1865-67), the American diplomat, statesman, journalist, and poet, John Hay (1838-1905) described her not long after her installation across from the Pavilon de Flore of the Louvre: 

"For the Sphinx with breast of woman
And face so debonair
Had the sleek false paws of a lion,
That could furtively seize and tear."

Photo: Phillip Townsend and Maura Gleeson

Here's the complete poem: The Sphinx of the Tuileries by John Hay.