Henri sits next to 3 phonetic neighbors — Henry, Heinrich, and Enrique are the closest matches by sound. Most share Henri's French-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"home ruler, lord of the house"
"pierce the valley"
"a musical lament (the linos song)"
"from the pool or marsh"
"power of peace"
"bright pledge, noble hostage"
"peaceful ruler"
"one who guards treasure"
"brave spear, strong with a spear"
"lord of the marches, borderlord"
"bearer of Christ"
"wealthy guardian"
"noise, tumult"
"ruler of the home"
"place of alder trees"
"crown, wreath"
"from the raven (place name)"
"graced by God"
"graciousness, kindness"
Similar sound: These names share phonetic patterns with Henri — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old High German origins, giving them the same cultural heritage as Henri.
Rhythm: Henri is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.