French electoral systems during the period of constitutional monarchy were varied and complex, with different electoral laws adopted in 1815, 1817, 1820 and 1831. You specifically asked about the reign of Louis Philippe, so I'll concentrate on the revised Constitutional Charter of 1830 and the Electoral Law of 1831.

Firstly the Constitutional Charter. In its original (1814) form, this provided that electors would have to pay a direct tax of at least 300 francs (art. 40), while deputies would have to pay a direct tax of at least 1000 francs (art. 38). That meant that there were (under the 1817 Electoral Law) about 90,000 men who were qualified as electors and about 16,000 who were eligible as deputies. These provisions were removed from the amended Charter that was promulgated in the midst of the 1830 revolution. Instead, the revised Charter mentioned only that deputies, in addition to being 30 years of age, should 'possess the other conditions prescribed by law' (art. 32) and that electors had to be 25 years of age and 'possess all the other conditions determined by law' (art. 34). In other words, the revised Charter downgraded the tax-paying requirement from a constitutional to a statutory matter. So, in answer to your question 'who decided on the census', Parliament did.

The relevant statute was the Electoral Law of 1831. This provided for the direct election of Deputies in 459 single-member constituencies. Although the number of constituencies in each department was supposed to be proportional to population and economic importance, there was no uniform rule of apportionment, and constituencies varied greatly in size.

All French men (not women) who were at least 25 years old and paid 200 francs in direct taxes were able to vote. In addition, some particular classes of persons, distinguished by former military service or scientific qualifications, had a lower qualification of 100 francs. This resulted in an electorate of around 166,000 people (up from 94,000 in 1830). It increased gradually, through economic growth and inflation, to nearly quarter of a million electors by the end of the monarchy in 1848.

To be a deputy, a man had to pay 500 francs in direct taxes (down from 1000 previously). It is estimated that this resulted in, at most, about 50,000 persons eligible to be deputies.

In terms of the electoral system, then, the 1830 revolution did little but extend the right to vote and the right to be elected from the tiny proportion of the very very rich, to a slightly larger proportion of the quite rich. The logic of the system was simple: that the property owners, who paid direct taxes, who had the most stake in society, should govern, and that the propertyless should be excluded. Since direct taxes were mostly on land, this meant that landowners were grossly over-represented in the Chambers, to the detriment of those who gained wealth in business or industry. The majority of electors (between 82% and 90%) were qualified by possession of landed wealth, while between 8% and 15% were qualified by virtue of industrial or commercial wealth.

Comparative bit: This was not limited to France. During the nineteenth century, these oligarchic electoral systems were also found in most if not all other European countries with free(ish) elections and functioning Parliaments - in Belgium, the Netherlands, Sweden, and later in the Austro-Hungarian Empire. In most cases universal manhood suffrage came only in the third quarter of the 19th century or later. France, which adopted universal manhood suffrage in 1848 and never looked back, was an early leader (although between 1852 and 1870 elections were constrained and not fully free or fair).

Electoral competition during the reign of Louis Philippe, under the Electoral Law of 1831, was hugely corrupt. According to Peter Campbell, 'The July Monarchy saw the most extensive electoral corruption that France had known, with the government, the candidates and the electors all in the market.' It should be noted that this was very much in line with the laissez-faire, enrichez-vous spirit of doctrinaire classical liberalism then in vogue.

My source for all the above is Peter Campbell, 'French Electoral Systems and Elections since 1789' (Faber & Faber, 1958), which provides more detailed exposition of every French electoral law than one could ever need.