This Berceuse is a characteristic example of French salon music from the late Romantic period by Adolphe Bouleau-Neldy. It features lush, dense harmonic writing typical of the era's lullabies.
Achieving an even, seamless tone in the flowing sixteenth-note accompaniment is essential for the cradle-song effect.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse (Op.61) is rated Henle level 4 of 9 — intermediate repertoire, roughly ABRSM grades 5–6. In the RCM system it corresponds to about level 5.
You should be comfortable at Henle level 4 — meaning you can already play level 3–4 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Berceuse (Op.61) lasts about 4 minutes.
Berceuse (Op.61) is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Ave Maria d'Arcadelt by Franz Liszt, Ave Verum Corpus de Mozart by Franz Liszt, Am Rhein by Heinrich Hofmann — see the full similar-pieces list on this page.