The feelings of love that a young person has for somebody else and that adults do not think is very serious is called "puppy love". Is there an equivalent noun for the elderly? For example, in Greece, when an old person falls in love, in which case this love is not taken seriously by the majority, this love is called "old-age love".
I don't know of any terms that deliver specifically what you've requested. You might consider:
- Infatuation. No age implications, has a sense of obsessiveness.
- Crush (noun def. 2). Informal. Has some sense of childishness and is also transient or brief.
- Passing fancy. Not nearly as strong as love, no age connotations, short lived. However, the phrase is a bit antiquated sounding (to my ear, at least), so it might be appropriate for describing the elderly.
- Smitten (adjective). Includes those genuinely in love, no age connotations. Someone smitten, especially an older person (who we generally assume has experience and isn't as susceptible to powerful feelings as a teenager) has fallen in love hard and fast and has at least some of the characteristics of someone infatuated, though there's at least an equal chance they're "really" in love.
Honestly, it's quite acceptable to use puppy love the way you want, as long as you give enough context to make it clear who's experiencing the feeling. Though it's most commonly used with youth, the definition isn't restricted to them. Describing an elderly person or couple with it even gives the phrase some extra weight, by implying they were so stricken that they behaved as if they were teenagers again.
I am not aware of any commonly-used term in English for this idea. You could certainly make up a word or phrase, but you would probably have to explain it.
I think there's a cultural thing here. In the U.S., at any rate, I don't think people generally view love between old people as something not serious.