This piece is a gentle lullaby characteristic of the salon style popular in the mid-19th century. It is distinctive for its flowing harmonic motion and emphasis on a singing melodic line.
Focus on maintaining a consistent swaying rhythm while balancing the melody against the accompaniment.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse is rated Henle level 4 of 9 — intermediate repertoire, roughly ABRSM grades 5–6. In the RCM system it corresponds to about level 6.
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 lasts about 3 minutes.
Berceuse 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 Berceuse by Adolf Gutmann, Bolero by Adolf Gutmann, Ballade by Adolf Gutmann — see the full similar-pieces list on this page.