The simplest answer to your question is that 1) speeds have increased; but 2) speeds would have increased even more except Tour organizers have been consciously making the Tour harder in order to increase the drama, suspense, and entertainment value of the race. That makes comparisons of overall winner's speed quite complex when combined with normal variations in wind, weather, and team tactics during the race.

First, some historical background. Over time, the winner's average speed in the Tour has indeed increased, especially in the period of the early 1990's and some (including, for a famous example, Greg Lemond, himself a three-time winner of the Tour) have claimed that this is evidence of doping behavior in professional cycling. However, as one of the other answers showed, there is a strong relationship between distance and overall winner's speed. Here is a plot that shows that relationship in the post-WWII period through 2012:

The distance of the Tour has been decreasing due to the rules and regulations of the UCI (the Union Cycliste Internationale), which negotiated a limitation to the length of races and mandated certain numbers of rest days during the Tour with the Professional Riders' Association. From an historical perspective, these limitation were a response to charges that the difficulty of the Tour resulted in riders needing to dope simply to survive, and that by "easing" the stages and inserting rest days there would be less need to dope.

An effect of shorter stages (and higher speeds), perhaps paradoxically, is that race organizers have been increasing the difficulty of the stages; this is particularly noticeable in the other two "Grand Tours", the Giro d'Italia and the Vuelta a Espana but also applies to the Tour: the number and "spacing" of categorized climbs in the Tour has resulted in more difficulty overall. Each year, at the announcements of the routes for each of the Grand Tours, riders and analysts pronounce whether a particular parcours will be relatively difficult or relatively easy, and favoring either sprinters, time trialists, or climbers. That there is a still a strong relationship between length of the Tour and overall speed simply means that the organizers haven't completely compensated for the distance effect with increased difficulty.

And, although your question was not expressly about doping behavior in the pro peloton, a bit more must be said about that. The plot above shows a clear relationship between distance and speed but there is still a question about deviations (or the "residuals") from that relationship. That is, after removing the effect for the length of each Tour, what is the remaining trend in the winner's average speed? The plot below shows that trend with a dotted red line.

As you can see, the winners' average speeds in the 1970's and 1980's were below trend, while speeds in the 1960's, 1990's and 2000's were above the long-term trend. So, even if the long-term trend in speeds can mostly be explained by Tour length (the correlation between Tour length and winner's speed is about 0.8), some have pointed to this secondary effect in the residuals as further evidence of doping. However, there are two counter-arguments, one slightly weaker and one very much stronger. The weaker argument is based on the observation that the residuals are "double-peaked" and speeds in the 1960's were also higher than the trend, then dropped in the 1970's and 1980's. If doping were the simple explanation, one would have to explain the drop in the 1970's and 1980's, not just the rise in the 1990's and 2000's. However, the stronger argument is based on examining data from other races and comparing them to the Tour. If one were to examine the residuals from a similar plot of speed vs. distance for the Giro and Vuelta, one would see that the years when their speeds were above (or below) their own trend lines did not correspond with the same years for the Tour. That is, the speed residual for the Tour and the speed residuals for the Giro or Vuelta are not "synchronized." Thus, if doping behavior explained the reason why Tour speeds were higher than would be predicted from distance, then one would have to explain why doping behavior was different in the Tour and Giro (or Vuelta) in the same year, often with the same riders. Below I include a plot that shows the "residuals" from the Tour (that is, residuals from the regression of winner's average speed on Tour length) plotted against the same residuals for the Giro. This does not mean, of course, that there is no doping in either the Tour or the Giro -- it simply means that one cannot use average speeds as evidence of that doping. Conversely, it also means that one cannot use doping as an explanation for increased average speed. Taken together, it does support the evidence that race organizers's decisions about the routes is a main determinant of the average speed.