This piece by French composer Sylvio Lazzari is a gentle, introspective cradle song. It is distinguished by its delicate melodic lines and harmonic textures typical of late Romantic salon music.
Focus on maintaining a smooth, singing tone in the upper voice against the flowing accompaniment.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse triste 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 triste lasts about 3 minutes.
Berceuse triste 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 Albumblatt by Carl Filtsch, 'Break, break, break' by Alfred Humphries Pease, All'amica lontana by Adolfo Fumagalli — see the full similar-pieces list on this page.