This sounds a lot like my grandmother's recipes: she would use "cuillerée" to refer to any spoon that was at hand, usually a tablespoon. She would also use "poignée" (handful) and "pinçée" (pinch).

Most English recipes I read use one of these terms depending on the amount of the ingredient that is actually being used. Maybe you could figure out from the recipe how much is actually needed, or being used, and then from this work out which size of these commonly used measurements is required in yours.

http://homecooking.about.com/library/weekly/bloldconvert.htm
http://en.wikipedia.org/wiki/Cooking_weights_and_measures
http://wiki.answers.com/Q/If_one_tablespoon_equals_three_tea...

A dessert spoon is a spoon designed specifically for eating dessert and sometimes used for soup or cereals, it may also be used to mix fluids. Similar in size to a soup spoon (intermediate between a teaspoon and a tablespoon) but with an oval rather than round bowl, it typically has a capacity around twice that of a teaspoon. Abbreviation: dstspn.

The use of dessert spoons around the world varies greatly; in some areas, they are very common while in other places the use of the dessert spoon is almost unheard of—with diners using forks or teaspoons for their desserts instead.[1]

In some traditional table settings, the dessert spoon appears above the plate, separated from the rest of the cutlery, or it may be brought in with the dessert.[2]

As a unit of measure, a level dessertspoon equals two teaspoons or 10 milliliters (about 3 fluidrams).[3] Though for dry ingredients, a rounded or heaped spoonful is often specified.

Sources

^ Martin, Judith (March 13, 2005). "On the Offensive". The Washington Post.
^ "The Secret of the Formal Place Setting". Diner's Digest. CyberPalate LLC. 1997.
^ Rowlett, Russ (October 30, 2004). "D". How Many? A Dictionary of Units of Measurement. University of North Carolina at Chapel Hill.

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Note added at 55 λεπτά (2011-05-01 12:39:38 GMT)
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yes. "spoonful" is VERY HEPFUL if Wwe are talking about cookery measurements...

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Note added at 1 ώρα (2011-05-01 13:14:34 GMT)
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in this case the French texte will be mentioned right next to the word cuillerée the size of the spoon or the use of the spoon. for example: La cuillère à café ou petite cuillère, cuillere à soupe etc.

in culinary language and books of cuisine, a spoonful is always a soup spoon size, unless other type of spoon is mentioned. Therefore I believe nothing has to be detailed further about which kind of spoon it is.
Even then one can aways discuss whether the product has to be equal flat to the spoon or with a little hill of product. In fact, here is the difference between a good cook and another: interpretation of sizes and volumes.

From my experience of FR recipes, I would say that the usual, default measure would be cuillère à soupe or (roughly) tablespoon; note, however, that the standard FR 'tablespoon' is in fact take as 10 ml, which really and truly equates to the EN 'dessertspoon' (En tbsp = 15 ml) However, to be honest, the difference is almost always fairly negligeable, especially in recipes that use such inherently imprecise measures!

You can, of course, also check the plausibility of this solution, simply from the logic of the recipe: ingredients like oil, flour, etc. are commonly used in tablespoon-sized quantities, whereas if it said 'piment de cayenne,' for example, then one would be more likely to expect a cuillère à café (tsp.) So that ought to give you a double check, if one is needed.

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Note added at 4 heures (2011-05-01 15:46:28 GMT)
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As I've said, the commonest (default) cuillerée in FR really equates to the dessert spoon, which is, however, much less common measure in EN, hence why I would recklessly suggest tablespoonful (tbsp.) as being near enough for all practical purposes, especially if the recipe isn't more precise in the first place.

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Note added at 18 heures (2011-05-02 06:33:15 GMT)
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Yes, MP, if you feel that people these days are likely to have dessertspoons, then by all means why not; my only concern was that the dessertspoon is much less commonly used as a homely measure in the UK (don't know about the US?) than the grande cuillère / cuillère à soupe in FR.

Do note that, whatever solution you adopt, I would avoid using soup-spoon in EN, since AKAIK that definitely is not usually used as a measure in an EN kitchen, and might indeed cause people some confusion.

Another solution might be to say 'a scant tbsp' — I think most people would understand that as 'a bit less than...', and in the case of a tbsp, that would amount to the same thing, really.

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Note added at 18 heures (2011-05-02 06:37:05 GMT)
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Now that you have given those vital extra context examples in your comment to Sheila's answer, it is clear that these must be 'grande cuillère' — there's no way you'd measure out cream using a teaspoon, for example.

Also, note that a 'grosse cuillerée' actually means something rather different since it doesn't refer to the size of the spoon itself, but to the extent to whcih it is filled: 'a good / generous / heaped spoonful'; I'm willing to be you haven't got any of these 'grosse cuillerées' for anything liquid!

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Note added at 18 heures (2011-05-02 06:39:18 GMT)
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Apologies for the typos:

"which"
and
"I'm willing to bet"

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Note added at 20 heures (2011-05-02 08:34:53 GMT)
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I think there's pretty much unanimity amongst those of us living in France and immersed in this culinary culture, which I'm sure will only be corroborated by our FR native colleagues.

I've just asked my Belgian partner, who is however a professional rather than domestic chef, and he confirms that he too would understand the default 'cuillerée' to be a 'cuillère à soupe'

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Note added at 21 heures (2011-05-02 08:45:52 GMT)
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Gilla has raised an important point, as to how we would normally express this in an EN recipe: one would indeed be much more likely to see '3 tbsp', for example, and only write 'spoonful' within the instructions, to say, for example: "Using just one spoonful of the olive oil, ..."

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Note added at 22 heures (2011-05-02 09:58:17 GMT)
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In the light of the extra context (examples) rpovided by Asker, I am now more confident than ever that this is indeed referring to 'grande cuillère', which as Sheila says equates more to the measurement of a dessert spoon.

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Note added at 22 heures (2011-05-02 10:06:35 GMT)
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I think the other answerer was unaware of the fresh examples you'd given, which pretty much clinch things.

Although I agree that EN recipes do often give literal measurements (not least, because they often give imperial + metric!), there is an argument for keeping the 'homely' measures as being more practical for the cook.
So I vote for 'dessertspoon' if you want to be strictly accurate, or 10 ml as suggested by Sheila if you want to go down that route — but this might involve you in converting other measures too, and also, what about the use of metric / imperial?

To be honest, the +50% difference is unlikely to make all that much difference in most recipes, since if this homely measure is used in the first place, it clearly means we are not talking about high-precision laboratory recipes. i can think of few dishes where the difference would be truly significant, unless the error accumulates seriously because there are 20 spoons of something, for example. But as you and I both know, who cook without recipes, it's much more about 'bit of this and a dash of that'...

You could, of course, always convert your measures to ml, and then convert them back to 'proper' tbsp'; so your 6 c. of tomatoes becomes 4 tbsp, etc. But frankly, I don't think it's very necessary, except perhaps for certain recipes that you could decide for yourself.