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"
"who is like God? (rhetorical — implying no one)"
"elf ruler"
"noise, tumult"
"nobleman of the second rank"
"yew warrior, bow warrior"
"brother, kin"
"flax, flaxen-haired"
"priceless, praiseworthy"
"trickster, shapeshifter"
"alder tree"
"victors garland"
"divine spear, god's spear"
"ruler of the home"
"bear"
"brotherly, genuine"
"firm, unwavering"
"pleasantness, delight"
"the fifth"
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.