Napoleon left Paris in the wee hours of April 13, 1809, in the Imperial coach, and arrived in Donauworth in the early afternoon on the 17th. [Update #2: Dawn on the 17th, not early afternoon, so about 8 hours less travel time.] He stopped only to rest and feed the horses and to eat, choosing to sleep in the carriage while travelling. This makes a total travel time of about 108 hours.
Update #2 - This paragraph copied from comments below:
The Imperial Guard was en route from Spain and arrived some weeks later; it did not accompany Napoleon. According to Thunder on the Danube (page 159): Napoleon travelled only with his personal guard; the Imperial carriage; and Josephine as far as Strasbourg. He stopped a handful of times to reassure allies (Kings of Wurttemberg and Bavaria) and meet with his niece, the Oudinot family and a couple of others. In the absence of his own guard the Wurttemberg Guard escorted him through that territory.
The road distance today is listed as 762 km, so let's take a figure of 850 km for two hundred years ago. This direction of travel was along major trade routes from France into Central Europe, as well as along the major invasion route into (or out of) France from Central Europe. There is no reason to believe that the route was substantially less direct then than now.
As an aside, the network of metalled roads (pikes) was expanding across Europe through this period. The Turnpike Act in the UK (allowing the establishment of private metalled toll roads) was already 100 years old by 1770. One might reasonably expect that similar arrangements existed in the larger nations of 18th century Europe: France, Prussia, Austria-Hungary, Bavaria, though I cannot track down explicit sources for this. (Eastern Europe was a different story, which might explain why travel from Berlin to Vienna went via Leipzig.) Certainly by 1809 Bavaria was criss-crossed by a network of Pikes that both Napoleon and Charles endeavoured to make use of.
John H. Gill's 1809 Thunder on the Danube Vol. I describes Napoleon's journey in the first several paragraphs of Chapter 5.