The French constitution of 1946 (Fourth Republic) established proportional representation (at the level of each departement). This regime was marred by considerable instability (24 governments in 12 years, not counting the provisional governments immediately after the war) as coalitions were made and unmade, a common phenomenon in proportional assemblies (such as in Italy).
The reform leading to the establishment of the Fifth Republic in 1958 was to a large extent motivated by this political instability. The 1958 constitution was tailored for de Gaulle (who became president first by a vote of the assembly, then after a constitutional revision by popular vote, which had not been done in France since 1848 when the elected president would three years later become emperor), and gives the president some actual political power; the Fifth Republic is often said to be a semi-presidential regime.
The 1958 constitution established majority vote for elections to the Parliament, which led for the most part to only major parties being represented in Parliament, and in particular to the de facto exclusion of extremes (both right and left). Majority vote was not new in France, indeed all regimes until 1945 had majority votes for the legislative assembly (if they had such votes at all), except between 1919 and 1929 when parliamentary elections followed a hybrid system in which candidates above a vote threshold were elected and the remaining seats were attributed on a proportionality basis with a per-department bonus for the winning list.
The Fifth Republic achieved the expected political stability, which made majority representation largely approved (if not consensual) among the political establishment as well as outside it.
In 1986, the government changed the parliamentary election rules to proportional representation, in the hope of lessenning their defeat. The incumbent party nonetheless lost the majority. The winning party in the 1986 election restored the per-seat majority system, only to lose power in the 1988 election. This gave the appearance that changing the rules was only about retaining power (and an ineffective way at that), cooling any ardor for reform.
Today some center to left-wing parties advocate the establishment of proportional representation, as well as the extreme right. Unsurprisingly, it is the parties who have the most to gain (because they lack local implantation on a large enough scale to win many legislative districts, yet have a significant following all over the country) who are the most fervent supporters of proportionality. Again, this gives the appearance of serving politicians rather than serving democracy.
So you have it: in a nutshell, the reason is largely historical, rather than arising from considerations on democracy or the lack thereof.
Note that plurality elections in France follow a two-round system, not first-past-the-post. The two systems lead to significantly different tactical voting. Voters can express preferences between “minor” candidates in the first round and select their favorite remaining candidate in the second round. Candidates can ally between rounds (there is no formal system for that, but a candidate can resign and encourage voters to pick one of the other remaining candidates).