The answer is "sometimes, depending on the context". In short, the longer a region had been populated and the higher the population growth, the smaller the average sized farm became. As populations increased, so did the demand for land, and this resulted in both initial expansion to wasteland and later fragmentation of the better land in the more densely populated regions. This fragmentation could occur from either dividing the land for inheritance or from the alienation of parts of the land for whatever reason.

One example would be Carolingian France in the 9th century (I've converted the Carolingian land areas into acres for ease of use, so rounding areas leave some minor gaps):

Size of Holding (acres)	Paris (%)	Seine (%)	Mauldre (%)	Upper Seine (%)	Eure (%)	Western (%)
0-9.9	26	22	11	15	2	5
10.2-20.1	45	50	30	26	13	28
20.4-30.3	18	17	36	12	4	29
30.6-40.5	7	4	13	6	12	12
40.8 or greater	4	7	10	41	69	26

While there are definitely a number of factors that effect the size of farms, such as different soil conditions and the reliance on other agricultural activities, there is something of a correlation between where the farms are and the proportion of small holdings. Generally speaking, the areas that have the highest population densities (such as those near a major town) and those from the oldest communities have the highest proportion of small holdings and the smallest proportion of the highest. In more distant regions, such as Hainault, the smallest farms could be more than 40 acres. Closer regions such as Artois, though still relatively undeveloped, could see a fluctuating average size of from ~30-40 acres. Compare that with an average of ~15 acres for the areas closest to Paris.

Looking ahead somewhat, we find that in 1305 the abbey of St. Bertin sixty farms at Beuvrequen and 62 farms elswhere. Of the farms at Beuvrequen, 43% were 5 acres or less, and of the farms elsewhere, a staggering 73% were 5 acres or less. 27% of the farms at Beuvrequen were between 5 and 10 acres, and 13% of those elsewhere. Only 6%, in both cases, were 20 acres or more.

This was an extreme case. In eastern England at the end of the 13th century, the land holdings of villeins was as following:

Size of Holding (acres)	Number	Percentage
<7.4	4687	29.5
7.4	1378	8.6
14.8	5724	36
29.6	3940	24.8

29.6 | 173 | 1.1

In 11 hundreds where the number of freemen and villeins are both known, freemen overwhelming own more of the smallest holdings with 46.5% holding <7.4 acres compared with 28.9% of villeins. Only when it comes to the 1/4 virgate (7.4 acres), do we see freemen holding more than the villeins (13.1% vs 9.2%). I haven't come across anything just yet to explain why villeins typically held more land than freemen in this period, but it likely had to do with the nature of land held by serfdom.

While there probably isn't much of a real difference in proportional farm size between the regions closest to Paris in the Carolingian examples and the eastern English example of the late 13th century (it's hard to tell without going back to the original data and redoing everything on the same scale), this could be masked somewhat by differing levels of cottars in each.

Nonetheless, in areas not heavily developed in the Early Middle Ages, the consensus is that land holdings became considerably fragmented and the average size of a hold was greatly reduced.

One part of the reduction in size has often been attributed to increases in crop yields, though this has been challenged on a low level a couple of times now. Effie Buck suggested that the traditionally accepted yield of around 2:1 for most seed crops, necessitating the cultivation of much larger areas, is based on flawed methodology, as it came from only a single reference point, a royal demesne, and the stored grain from the previous year indicates a larger crop the year before. Jonathan Jarrett has reached a similar conclusion, suggesting that the traditional reading of the Carolingian text is wrong and that the harvest was already mostly distributed.

As most areas where we have reliable long term data from show that a yield of between 3 and 4 to one remained essentially unchanged for hundreds of years after record keeping began, I can readily believe that this is the case. However, the fact that larger farms in Carolingian times were typically sown at lower rates than the smaller holdings may go some way to explaining how smaller holdings were viable once three field rotation became more common and why larger holdings might have been split up as inheritance or need demanded and initially kept the same output as before.

Another factor to be considered is the manuring and treatment of the soil with lime or marl in some regions where the demand for grain was high and the prices consequently raised. Here the yield could exceed 6:1, and sometimes even reach above 10:1, although this was a combination of good soil and the treatment. This would allow for much smaller holdings to be viable (perhaps 5 acres for a family). Without the high wheat prices, though, it was mostly uneconomical to systematically manure and marl the fields on a regular basis. Mostly this would be done in the garden, where a cash crop might be grown in addition to vegetables and fruit for the household.

With average yields of 3-4:1, a family would need somewhere between 10 and 12 acres to survive, depending on the conditions of the area. On this basis, perhaps 2/3 of villeins in 13th century would have been doing more than just surviving and nearly a quarter of them would have been thriving.

References

• Rural Economy and Country Life in the Medieval West, by Georges Duby
• The Agrarian History of Western Europe, by B.H. Slicher van Bath
• The Fontana Economic History of Europe, vol. 1, ed. by Carlo M. Cippola
• 2:1 against: the misconception about Carolingian cereal yields, by Jonathan Jarrett
• The Polyptych of Saint Germain-des-Pres: peasant agriculture and commerce in the ninth century Paris Basin, by Effie Buck