In the US 'lieutenant' is pronounced as 'loo-tenant'. In the UK it is pronounced as 'leff-tenant'. The French, whose word it is originally
after all, pronounce it more closely to the US version than the UK one; at least, there's no F sound. How has this come to be?

This is an excellent question, one I've often asked myself.

The sound [u] (or in its weakened semi-vowel character as [w]) at the end of the first syllable requires strong lip rounding. If carried to extremes, this lip rounding can lead to a noisy, rather non-vocalic sound source, which is acoustically much like the fricative [v]. This kind of sound change has happened countless times in the history of all of the world's languages. From a [v] to an [f] there is only the further step of devoicing the [v] by assimilation to the following voiceless stop, [t].

A near parallel in English is the alternation seen in "Shaw/Shavian". Here, the bilabial fricative doesn't become devoiced, because it is intervocalic, an environment unfriendly to devoicing.

In Old French, both 'lieu' and 'luef' were used to mean 'place', the latter more rarely. English seems to have adopted the SOUND of one of the old words and the SPELLING of the other, whereas Americans etc ended up with the matching pair, with the spelling as extended, more or less, into modern French. Certainly, the Scottish poet, John Barbour, wrote of a 'luftenand' as long ago as the mid 14th century.

It could be as you say, MQ (and welcome back, by the way! Where have you been?).

But French lieu < Latin locus (cf. French feu, from Latin focus) had no "f" in it originally. If this sound did develop in some French dialects, it did so as a result of the kind of increased lip rounding I referred to above. The same phenomenon has occurred widely in language history, so it is an open question as to whether the change from [u] to [w] to [v] (and finally to [f] before an unvoiced stop, as in lieutenant) happened independently in English, or was borrowed, as you suggest, from some French dialect in which the change had already occurred.

Dear Maiku, I still occasionally look in, but there's generally little to be 'done' here. I noticed a watershed near the beginning of the month...the site had been running for some 246 days and exactly that many questions had been posted in 'Words & Language'...an average of one per day.
Given that there are, I suppose, about 20 regular responders here, the chance of finding a question to contribute something new to is remote. This is compounded by the fact that most questions are set and initially answered during what one might call "American Computing Hours". 6 pm in NY and midnight in LA = bedtime and getting-up time in UK! Consequently, the occasional cameo appearance is about all we Brits can hope for. (This isn't a complaint, by the way..."I'm just tellin' it like it is, man!") Cheers