It certainly appears to be the bit of an outboard that is in the water:

Des modèles sont offerts avec vérin d'assistance pressurisé au gaz qui réduit considérablement l'effort requis pour LEVER LE PIED DU MOTEUR HORS DE L'EAU. ...
www.honda.ca/MarineFre/Models/20-15_hp/BF20.htm?page=produc...

La plaque anti-cavitation du pied du moteur devrait se trouver SUBMERGEE de quelques cm (1-2 po) dans l'eau. Si elle se trouve à l'interface de l'eau, ...
www.i-services.net/membres/forum/messages.php?uid=20021&sid...

Elle est aspiré par des grilles en bas du pied du moteur du COTE DE L'HELICE. Pour réussir à la faire monter au niveau du moteur, il y a une pompe à eau qui ...
fr.answers.yahoo.com/question/index?qid=20080611010536AABYRtn

Ensuite, la TRAINEE imposée par le pied du moteur lorsqu’on navigue à la voile n’est pas négligeable; pour éviter cette traînée, il faudrait sortir ...
www.capehorn.com/sections/remotorisation/remotoriserFr.htm

This insurer calls it the engine shaft, though I would have thought that would be the bit between the engine (above water) and the outdrive/lower unit :
Type, marque, modèle du PIED MOTEUR: (Alpha 1,2,3, TRS, OMC, Bravo 1,2, etc.)
www.lapointefils.com/francais/bateaux.htm

Type, make, model of ENGINE SHAFT: (Alpha 1,2,3, TRS, OMC, Bravo 1,2, etc.)
http://www.lapointefils.com/english/boat.htm

And then we get "lower unit" and "outdrive" :
Bravo LOWER UNIT Seal Kit, 18-2645. Part# 82540 | Mfr. Sierra | Mfr# 18-2645 ... Lower Drive Shaft For all Alpha I Gen II (s/n OD469859-OK999999) drives ...
www.go2marine.com/category.do?no=13618&mfrno=350

MerCruiser bravo outdrive LOWER UNIT gear housing w/oil. C $533.84, Buy It Now ... MerCruiser Top cover 11TR\TRS\Alpha SS\SSM 11\111\1V\V. C $26.68 ...
stores.ebay.ca/ShipWreckSalvage-Supply-and-Parts

LOWER UNIT zinc, evinrude and Johnson Outboards, 55 to 75 HP, ...
www.thefind.com/sports/info-hp-evinrude-outboard

OUTDRIVE
The LOWER UNIT of a stern-drive motor that houses the drive gears and to which the propeller fastens.
http://www.discoverboating.com/resources/glossary.aspx?key=O

How do I install the Briggs and Stratton motor to drive the LOWER UNIT of an outboard boat motor? I am interested in also setting it up to ...
cr4.globalspec.com/thread/17882/B-S-Motor-to-drive-out-board-motor-lower-unit

This LOWER UNIT resembles the bottom part or lower unit of an outboard. The outdrive or lower unit part also swivels ...
www.boatingbasicsonline.com/course/safety/3_6.php

A stern-drive engine is attached through the transom to a drive unit (also called an "OUTDRIVE") that is essentially the LOWER UNIT of an outboard. ...
www.boat-ed.com/mn/course/p1-4_whatkindofengine.htm


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Note added at 23 mins (2008-08-18 00:32:27 GMT)
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What you see in the picture is the lower unit, as it were, only inverted, of a diving sperm whale.