Correct Japanese. Also the title of roughly nine hundred ballads.

What a Japanese person actually thinks
Reads like a karaoke song title or the tagline on a wedding-hall brochure. Completely sincere, completely unsurprising. Nobody will laugh; nobody will be moved either.

Meaning

Literally: eternal + love
Actually: Eternal love. Says exactly what it says.

Scores

Naturalness●●●●●

Perfectly natural Japanese. This is a real, common phrase.

Coolness●●●●●

The Japanese is fine — the problem is that it's a greeting-card sentiment in any language, and the kanji don't make it deeper.

Watch out

lowIf this is about a specific person, consider that 'eternal' is a strong claim to have needled into you permanently.

Get this instead

永久 towa
eternity

Same idea, two characters, and read as 'towa' it's noticeably more poetic than 'eien'.
縁 en
the karmic thread connecting people

A single character for the bond between two people that was meant to be. Far more interesting than 'eternal love', and very Japanese.

On skin

永遠の愛

Orientation: vertical

Mincho. Something restrained will fight the sentimentality a little.