I'd suggest that there were two key factors in the hesitation of Blum's government in supporting the Spanish Republic:

• Britain. The over-riding aim of French foreign policy in the 1930s was securing a guarantee of military cooperation from London in the event of war with Germany. French politicians were therefore highly concious of British attitudes and wary of opening a gap between the two countries. British reservations over Spain were communicated to Blum from the outset of the crisis (via Eden), something maintained by Ambassador Clerk throughout the crisis.

• From within. The Popular Front was obviously a coalition and not a particularly stable one. The Radicals in government largely opposed intervention, being wary of the risk of escalation and its reception by the high-charged French Right. From this flank the charge against intervention was led by Delbos, Chautemps and Herriot - all powerful political players. Those Radicals in cabinet that did support intervention (Cot and Zay) were a younger but less influential breed. (Daladier wavered.) Nor was it a straight split: the strong pacifist wing of the Socialists (led by Faure) were also opposed to intervention, for obvious reasons.

People have argued about the various weight that should be assigned to each of these but both need to be put in the context of a government under immense pressure to both hold itself together and to reassure the 'middle' of French politics that it wasn't a radical band of anarchists. Ultimately, Blum wasn't willing to risk a fall of government (a real possibility) or a civil war (less real) over Spain. Hence the compromise solution of the Non-Intervention Agreement.

(And, just to note, the extent of French intervention was never intended to be more than facilitating Spanish arms purchases and deliveries. By mid-1937 Blum was turning a blind eye to the illegal arms shipments to Spain being organised by some of his ministers.)

Source: I'm a big fan of Julian Jackson's The Popular Front in France.