This is going to vary extraordinarily over time, after the invasion of Russia Napoleon's Grand Armee was left with virtually no horses due to the attrition and an inability to acquire enough replacements due to a number of factors.

Lets say around 1806 then, the battle of Jena. We'll use Napoleons Grand Armee in the field rather than taking the collective sum of all of the National Guard and militia units in French service as well as the armies deployed in garrisons or elsewhere.

The Grand Armee before the campaign consisted of some 160,000 men including gunners. Of which 32,000 were cavalry of various types. So a ratio of 4/1 if artillerymen are counted as infantry. At the height of the campaign the army numbered some 300,000 men.

The Prussian army was stated to have some 171,000 men of which 35,000 where cavalry, 121,000 infantry and 15,000 artillerymen. So an Infantry/Cavalry ratio of 3.5/1. Like the French though the Prussians had many more men in reserves and garrisons, approximately 83,000. Plus a number of Saxon soldiers.

So factoring for artillerists in the French army the ratio is likely roughly 3.5/1 for both.

At Waterloo in 1815 we can examine the Anglo-Allied, French and Prussian field armies.

The Anglo Allied army at the battle of Waterloo (excluding the men who were deployed at Hal who did not participate and casualties suffered at Quatre Bras) numbered some 53,850 infantry and 13,350 cavalry of all types. Resulting in an Infantry/Cavalry ratio of 4/1

The Armee du Nord at the battle of Waterloo (excluding Marshal Grouchy's Corps at Wavre and the casualties from Quatre Bras) numbered some 53,400 infantry and 15,600 cavalry. For an Infantry/Cavalry ratio of 3.4/1.

The Prussian army at the battle of Waterloo (excluding the casualties caused by the battle at Ligny and III corps at Wavre) numbered some 58,300 infantry either at the battle or en-route and 10,000 cavalry either at the battle or en-route. For an Infantry/Cavalry ratio of 5.8/1

It should be noted that whilst the total numbers of cavalry and infantry of each nation will number substantially higher I think that it is more accurate to look at the numbers that are able to be brought to battle effectively. 3000 untrained cavalry recruits or a Regiment of Cavalry deployed on necessary garrison duty should not count towards the total. For example the British cavalry regiments would nominally leave 1 squadron at depot when they were deployed overseas.

For the moment these are the only statistics immediately available to me however I will attempt to find exact numbers for other armies and nations throughout the Napoleonic wars. The French Grande Armee's invasion of Russia in 1812 and both the French and Russian armies composition at Borodino. Also the Battle of Wagram in 1809.

Sources

Jena, 1806 - David G Chandler

The Waterloo Companion - Mark Adkin

Wellington's Light Cavalry -Bryan Fosten

Edit, cleaned up my post a bit.