Calque pairs like 'praeternatural/metaphysical'

Solution 1:

Eau-de-vie (< French eau de vie < Lat. aqua vītae)
and
Akvavit/aquavit (< Scandiwegian akvavit < Lat. aqua vītae)
and
whisk(e)y (< abbr. ‘whiskebae’/‘usquebaugh’ < uisce beatha [Irish] / uisge beatha [Scottish])
— all types of locally important, strong alcoholic beverages meaning ‘water of life’.

Vladimir (< Slavic vladi- + mir¹)
and
Henry (< Germanic heim(i)- + rīkaz)
— ‘rule the world / ruler of the world’

Benedict(ion) (< Latin bene + dict(iōn-) < dicō)
and
euphem(ism) (< Greek εὐ- + φήμη < φημί)
‘well-speaking’ / ‘something well spoken’

(I’m sure there are many more, just can’t think of any off the top of my head)

¹ If we choose to believe that it is indeed from mir, rather than from *mēr ‘greatness’.

Solution 2:

How about quintessence and Pentium? They both mean "the fifth element".

quintessence (< Latin quint-us/a, fifth + essentia, (classical) element)

Pentium (< Greek pente, five + -ium, suffix for chemical elements, after the style of early-named elements like helium)

Solution 3:

Melancholic – gloomy [Greek melanos- black khole- bile]
Atrabilious – ill-natured, spiteful [Latin atra- black bilis- bile]

Magnanimous [French magnanimite magnus- great animus- breath]
Mahatma [Sanskrit maha- great atman- breath]
Both literally meaning great-souled but with difference in application.

Theodore [Greek god’s gift]
Jonathan [Hebrew god gave]

kamikaze [Japanese Kami (divine) kazi (wind)]
typhoon [Chinese Tai (great) fung (wind)]
[Reckless, destructive person or attack / violent storm]

Solution 4:

From least to most interesting:

putsch and coup

[does not meet the dual root critierion, but both mean 'slap'/'attack' in German and French respectively]

Also

troika and trinity

both with the roots 'three' + 'set of'

preface and prologue

preface: 1350–1400; Middle English prefas, which is from Old French preface (from which derives the modern French préface), from Medieval Latin prefatia, for classical Latin praefatio (“a saying beforehand”), from praefor (“to speak beforehand”), from prae- (“beforehand”) + for (“to speak”)

prologue: [from Latin prologus, from Greek prologos, from pro-2 + logos discourse]

chirography [handwriting, penmanship] and manuscript

[Greek hand + writing; Latin hand + writing]

bacchanology and Festschrift

bacchanology: The study of drinking and its preparations, and history. (bacchanalia = drunken feasts) + (logos = study/writing)

Festschrift: a volume of writings by different authors presented as a tribute or memorial especially to a scholar. German, from Fest celebration + Schrift writing

kamikaze and spiritus sanctus

[from Japanese, from kami divine + kaze wind, referring to the winds that, according to Japanese tradition, destroyed a Mongol invasion fleet in 1281] [sanctus: consecrated, sacred, inviolable, venerable, august, divine, holy, pious, just; spiritus: breath, breathing; light breeze; spirit, ghost...]

Solution 5:

An interesting example, in that the meanings are almost the same except for a subtle distinction in usage, is insectivorous and entomophagous (and the related forms insectivore, entomophagy, entomophage, etc).

Both words refer to the consumption of insects. The difference is that an insectivore (Latin insectum + vorare) is an animal or plant that consumes insects, while entomophagy (Greek entomon + phagein) usually refers to the practice of humans consuming insects (here is a typical example).

A few more usage notes: Insectivorous is the more common term, and seems strictly applied to non-humans - or at least I can't find any source in which (modern) humans are described as insectivores. Entomophagous, on the other hand, is occasionally applied to animals - for example, see this article on entomophagous parasites.