The French proverb implies that the expression of love indicates the sole reality of love.
The proof is in the pudding
that the real worth, success, or effectiveness of something can only be determined by putting it to the test by trying or using it, appearances and promises aside—just as the best test of a pudding is to eat it.
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The old English proverb, "All the proofe of a pudding, is in the eating," has been clipped to the head-scratching "The proof is in the pudding."
The proverb has a fascinating etymology. I will quote some at length the Wiktionary entry.
This proverb dates back at least to the 14th century as "Jt is ywrite that euery thing Hymself sheweth in the tastyng", and William Camden stated it in 1605 in Remaines of a Greater Worke, Concerning Britaine as "All the proofe of a pudding, is in the eating", per Rogers' Dictionary of Cliche and the Oxford Dictionary of Quotations.
A 1682 translation of Nicolas Boileau-Despréaux Le Lutrin (written between 1672 and 1674) renders it "The proof of th' pudding's seen i' the eating."
The current phrasing is generally attributed to the 1701 translation by Peter Anthony Motteux of a proverb Miguel de Cervantes used in Don Quixote (1615), al freír de los huevos lo verá (“you will see it when you fry the eggs”).
The shorter form the proof is in the pudding, which is found in an 1867 issue of the British Farmer's Magazine, and came into common use in the United States in the 1950s, is becoming increasingly common, despite missing the point of the original meaning.
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To keep the context in realm of l'amour, there is a parallel thought in Lerner & Lowe's Show me, from My Fair Lady.
I rather like the first line quoted (by Eliza, who is sick of Freddy's romantic words).
Don't talk of stars Burning above; If you're in love, Show me!
Tell me no dreams Filled with desire. If you're on fire, Show me!
Here we are together in the middle of the night! Don't talk of spring! Just hold
Anyone who's ever been in love'll tell you that This is no
time for a chat!
Haven't your lips Longed for my touch? Don't say how
much, Show me! Show me!
(Source: All Musicals)