Chef is head for sure, see Grand Dictionnaire Terminologique :
"Note(s) : On parle ainsi d'un chef d'accusation, d'un chef de demande et, en particulier, d'un chef de préjudice, d'un chef de jugement ou d'arrêt. Chef n'a pas d'équivalent anglais unique : dans le cas d'un chef d'accusation, on parle en anglais de count, dans le cas d'un chef de demande, de head (of claim), dans le cas d'un chef de jugement, de finding."

But not sure about "conclusions".

These are arguments raised by the claimant in his procedure. So it could be that the court of appeal omitted to answer one of the "heads of the submissions" meaning one of the submissions of his claim. Or one of his arguments or pleading.

As I've stated previously, Canada reigns supreme when it comes to accuracy of legal terms in both French and English simply because the practice of both common law and civil law is sanctioned in French and English.

Extensive research has been conducted by the Quebec Research Centre of Private and Comparative Law, the end result being the publication in two volumes of "Private Law Dictionaries and Bilingual Lexicons" and updated editions.

The online version of Grand dictionnaire terminologique (http://www.oqlf.gouv.qc.ca/ressources/gdt.html) of l'Office québécois de la langue française and the Larousse indicate that the translation for "chef" = charge, count, indictment and "conclusions" = submissions, findings. "Chef de demande" is translated as "head of claim" which makes sense because the initial translation of "demande" is "request" and the initial translation of "conclusions" is "conclusions", "findings", "submissions".

Therefore, if we were to literally translate "ce chef des conclusions", we would arrive at "this count of submissions" which doesn't really make sense in English. Hence my reason for supporting "this particular submission".

The translation agency of the Ontario government has developed a very efficient bilingual legal terminology bank with respect to common law terms.

Elsewhere on this site, the bilingual legal tomes published by the Council of Europe is highly recommended. I haven't reviewed these publications but I have used the Research Centre's publication and have found it to be extraordinarily accurate.

The Quebec legal publishing house, Éditions Yvon Blais, has an excellent collection of bilingual and monlingual publications for purchase.

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Note added at 12 hrs (2009-05-09 07:07:52 GMT)
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Here's my initial suggested translation of "qu'en s'abstenant de répondre à ce chef des conclusions, la cour d'appel a violé l'article":

"that refraining from responding to this particular submission, the Court of Appeal has violated Article..."

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Note added at 19 hrs (2009-05-09 14:15:25 GMT)
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Writeaway, here's a direct text from le Grand dictionnaire terminologique defining "conclusions" in French:

Définition :
Acte de procédure par lequel le demandeur expose ses chefs de demande, le défendeur ses moyens de défense. C'est par le dépôt des conclusions que le débat est lié. Le juge a l'obligation de répondre à tous les chefs des conclusions.
.
.

. Note(s) :
Devant le tribunal de grande instance, seuls les avocats ont le droit de conclure pour le compte d'un plaideur et les conclusions ne constituent pas toujours un acte indépendant : l'assignation pour le demandeur, la requête conjointe pour les deux parties tiennent lieu de conclusions.

The basic tenets and foundation of common law and civil law are the same in both Canada and Europe. The differences lie in legislation and application thereof and terminology. However, basic terms, such as pleadings, submissions, arguments, claims, etc are common law terms which have the same meanings wherever common law is practised in the world or else it isn't common law. The same holds true for civil law.

The difficulties we encounter in legal translation arise because we are attempting to translate common law terms into French (which are non-existent because the French don't practise common law) and civil law terms in English (which are also non-existent). Hence the reason for the establishment of a research centre at McGill dedicated to developing bilingual standard terms for both common law and civil law.

I have found over the years that legal translations in Canada tend to be more accurate than in Europe simply because both types of law are practised here in both languages and terms have had to be developed in both languages.

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Note added at 19 hrs (2009-05-09 14:27:41 GMT)
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Michèle, I apologize for saying that your suggested translation wasn't accurate. What I should have said was that your explanation was accurate but your suggested translation was a bit convoluted. I believe that it suffices to say "particular submissions" or a similar term. There is no need to make any reference to this being an appeal of a decision made by a Court of Appeal simply because there is no reference to it in the text provided by the Asker. The only reference to "appeal" is used in "court of appeal". I prefer to translate the text as it presents itself, especially in legal translations which have to be accurate, and only offer up explanations in parentheses if I'm leaving a term in the source language for which there is no existing equivalent term in the target language.

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Note added at 20 hrs (2009-05-09 15:24:05 GMT)
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Writeaway, all I'm trying to say is that Canada lives both common law and civil law in French and English, especially in Quebec, and by sheer use, the Canadians have had to develop legitimate terms in both languages for both types of law. I don't believe there is any country in Europe (and I stand corrected if I'm wrong) which actively practises common law and civil law in both languages. For this reason, I fully support Canadian legal terminology. The research has been exhaustive, meticulous and in depth. I tend to find that less so in Europe in the area of law. This is all about translating common law terms into French, using French words that accurately express the English language meaning, such as the difference between a claim and a pleading or argument . They are not interchangeable terms.