Your found leaks will affect the power of the flute, especially the low register, so yes, it is worth fixing them. Even just greasing the stopper generously may suffice, or you can wrap a little PTFE plumber’s tape around it as a temporary, pre-renewal measure, or try steaming it at the spout of a boiling kettle, then greasing and reinserting. Old cork dries and shrinks, especially in an unused flute! Remember to set it correctly.
The Eb key will probably need a new pad and maybe some adjustment, but careful cleaning of the pad surface and tone-hole rim and checking the latter for damage and inspecting the closing action of the key may let you fix it. Check all the other pads, holes and key actions too.
The crack in the barrel CAN leak despite the metal lining - as the lining will not be continuous all the way through, even if the socket is lined (probable in a French flute) as the socket lining is separate from the tuning slide tube and because of how these things are made, cannot be soldered together, so air can pass between the metal parts where they butt together and leak through a crack in the wood. So suck test your barrel too. I bet it leaks! (The oft-seen eBay claim that a cracked metal lined tuning barrel wont leak is rubbish - but the folk who write it don’t know what they’re writing about…)
As others have said, French 5-key flutes of this type have a notoriously flat F#, even more so than English ones, and yes, you do have to vent the F key and the Eb key to improve them - and they still tend flat because the makers/players wished to keep available the Baroque forked F natural fingering. You can read up about French simple system flutes on Rick Wilson’s website so you understand your flute better.
You should also bear in mind that the majority of French flutes of this type were built for the diapason normal pitch standard, c A=432-5Hz, thus rather flatter than modern “concert pitch” - so you should ascertain whether your flute is one of those or one of the rather less common but identical looking ones which is built for c A=440Hz. - knowing which it is will affect your perceptions of its behaviour! If it plays just about at 440 or won’t quite get that high with the tuning slide fully closed, then it is a diapason normal (low pitch) flute if it will play at 440 with the slide open about 10-15mm, it is a modern pitch instrument. This also affects its practical value and what it is worth spending on restoring it.
As for getting it repaired/overhauled, where are you? Many of the makers on The List will undertake repairs if asked, or I do so and there is Jon Dodd in Ireland.