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Companies operate under a name. So if you want to have a phrase for the French, this would be it in my opinion

I would use this sort of wording the very first time it occurs (only!), just to make the link with what has presumably been set up in the Preamble ("The Company hereinafter referred to as..." etc.), and thenceforth just use the xxx name on its own — unless, of course, the specific names involved were such as to cause some kind of confusion (such as Mr. Jones and the company called Jones)!

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Note added at 2 hrs (2013-05-04 15:25:01 GMT)
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I wouldn't like to be categoric about this, as it's a bit outside my area, but I would say probably yes; the fact that this has not been mentioned in the 'preamble' probably explains why it is now being expressed like this throughout the document. That is one of the advantages of the 'preamble', in that it defines up front the relatively short-hand forms to be used from thereon in.

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Note added at 5 hrs (2013-05-04 17:42:23 GMT)
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Phil has got a point; if both (all) of the parties are referred to by their company name in full, then there really is no point in adding anything at all.

My only proviso would be if for some reason a rather long company name had been shortened, like 'the Peninsular & Orient Steamship Company, referred to as P&O' — in which case, I feel you might be justified to use my suggestion for the first occurrence only.

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Note added at 1 day3 hrs (2013-05-05 15:44:51 GMT)
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Asker, in the light of your added context, please disregard this answer; as PG and W/A have said, there is no real justification for attempting to render this in EN.