Luxembourg is of little concern to the great powers. Its position between France, Belgium and Germany means that it is part of the slightly more important Benelux Region. It has very little significance in the greater schemes of the great powers, and thus usually ends up as a footnote in history. Should a war break out between Germany and France, Luxembourg probably will be invaded because, like Belgium, it allows bypassing the heavily fortified French-German border. It's unlikely it would offer any major resistance.
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Being a democratic country, Luxembourg has a positive relationship with other Democratic countries (+10 to +20) and a slight negative relationship with everyone else (-10). It lacks colonies of any kind and does not hold any puppets at the start.
Luxembourg does not have claims or cores on foreign soil.
There is little hope for Luxembourg to survive in the face of her powerful neighbors: the German Reich, in particular, almost always use a focus to declare war on the BeNeLux to go around the Maginot line. Nevertheless, Luxembourg can greatly extend her existence by constructing land forts on its only province since day one. These forts, protected from being encircled and cut off from the capital, will end up more useful than the entire Maginot Line. Entrench as deep as possible, add a few artillery batallions, expand your army to no more than wide enough for the entire border (240), and try to cause as much casuality to your enemies as possible.
Another strategy for Luxembourg and her hope for survival is to become fascist and join the axis. When Germany invades France or Belgium, Luxembourg (as an ally of Germany) can send in what little troops she has, and can attempt to assist enough in order to gain enough war experience, and potentially take some counties in Belgium, maybe even in France as well. From there, it gets a little easier, as with more land come more factories, which will help her industry. Don't bother with naval, or even aerial research for that matter, as in the early stages it isn't that necessary, however, a good boost to the army would be paratroopers, researching paratroopers will make it easier to annex the Netherlands, and Belgium if the German Reich hasn't attacked yet. Even if an initial attack fails on Belgium and Holland, if Luxembourg is an ally of Germany, she can call the Germans in to assist and win the war.