Douglas, since the British have 18 pre-dreadnaughts in service to France's 8 and France is even more badly outnumbered in older ships I would put the odds of a French victory at sea, as opposed to commerce raiding, as being less plausible than a German High Seas Fleet victory over the British Grand Fleet during WWI.
The cut-off point for battleships of the time is very fuzzy, and picking numbers without taking care to examine the value of older ships is always tricky. Your numbers are really odd because there are 20-22 ships that could be legitimately be called pre-dreadnoughts in the Royal Navy at the time, but I can't figure out how to hit 18. Your number for France must discount the large number of older ships which were, by 1898, either finished or undergoing modernization with large numbers of quick-firing guns. These ships could certainly have stood in a line action, especially against some of the British vessels of a more questionable utility, such as the
Admirals.
Nor does it help that the French battleships are not only outnumbered but have serious problems. The five ships sometimes called the Charles Martel class were each the product of the designer of each individual ship, resulting in the same main armament but nothing else including armor and speed. The three ships of the Charlemagne class are barely 75% the size of their British counterparts and suffer from serious problems of stability plus a much weaker secondary armament than intended(reduced due to their size).
I have some knowledge of these ships. Though the problems with stability and a smaller secondary armament are certainly worthy of note, the comparison of displacements is not as relevant as you would think; a very large proportion of the British preponderance in displacement goes to their endurance (coal, stores, etc), and is not a measure of their value as fighting ships. In any case, I cannot emphasize the parlous nature of British gunnery before Captain Scott's reforms enough. Ropp notes that French gunnery was likely to land 50-100% more hits than the British at this point. This would be changed in a few short years, but the old bromides of higher British seamanship and better navigation skills were still in vogue at this point, and pretty paint was more important than firing drill.
but it is also the move most likely to provoke the British into harsher terms should it fail after doing enough harm.
If it fails, then it has not done enough harm. The problem will be that of the Napoleonic Wars; even if you grab Guadeloupe and Reunion and New Caledonia, that hardly matters when the British mercantile fleet is rapidly becoming the United States mercantile fleet. Everyone will find it much easier to come to an agreement when it becomes clear that Britain can't
really hurt France, and France (most likely) can't
really hurt Britain.
Strategically, the Royal Navy is positioned in a way that makes it difficult for you to get some hypothetical 18-8 matchup. Three new battleships are in China under Seymour to watch the Russians, one is on station as Jackie Fisher's flagship in North America, Stephenson has eight at Gibraltar to prevent a hypothetical joining of the squadrons of Barrera and Fournier at Brest and Toulon respectively, and Hopkins has seven or eight (depending on how you evaluate
Hood) at Malta which he has orders to keep there to watch the Levant against any Russian shenanigans, as well as to cover any merchantmen traveling through the Mediterranean.
A worst case scenario sees Fournier (who has the eight ships you must refer to) getting sandwiched by Stephenson and Hopkins in any foray, which is close to your hypothetical matchup at 15/16 to 8, though Fournier would have to be idiotic to allow this to happen to him, since he is closer to either British squadron than they are to each other.