Short answer. No. When you and your agent stipulated that he would be allowed only a certain sum for expenses, you are not liable for anything beyond that amount. The Civil Code lets principal and agent fix this ceiling by agreement, and once fixed, it caps what the agent can later demand for expenses.
What the law says
When it was stipulated that the expenses would be borne by the agent, or that the latter would be allowed only a certain sum.
Civil Code, Article 1918 — When the Principal Is Not Liable for Expenses. Read the full provision →
A fixed-amount stipulation caps the principal's liability
Article 1918 of the Civil Code lists the situations where a principal is not liable for expenses an agent incurred while carrying out the agency. One of them is exactly your situation: when the principal and agent stipulated that the agent would be allowed only a certain sum for expenses. Once that ceiling is part of your agreement, the principal's obligation stops there. The agent cannot fall back on the general rule that a principal must cover the agent's necessary expenses, because the parties already displaced that general rule by fixing the amount themselves.
Why the agreement controls
Agency is fundamentally a contractual relationship, and the fixed-sum arrangement is simply the parties exercising their freedom to define, in advance, what the agent may claim for expenses instead of leaving it open-ended. This protects the principal from open-ended expense claims and gives the agent certainty as well, since both sides know from the outset exactly what is being budgeted for the undertaking. The same article also recognizes the related situation where the parties agreed the agent alone would bear all expenses, which is simply the fixed amount taken to zero.
What this does not excuse
A fixed-expense stipulation only addresses reimbursement for the cost of carrying out the agency. It does not, by itself, affect the agent's separate right to compensation for his services if that was agreed on, and it does not shield the principal from other obligations the agency contract or the law may impose, such as liability the principal chooses to assume by availing of benefits obtained from a transaction. If the agent goes over the agreed amount without authority, the excess is generally his own to absorb, not an added claim against the principal.
If a genuine dispute arises
Disputes under this kind of clause usually come down to what exactly the parties agreed the fixed sum was meant to cover, and whether the expenses the agent is now claiming actually fall within, or outside, that scope. Because the cap exists only by stipulation, its wording in the agreement, rather than any general rule about agency expenses, is what will decide how much the agent can recover if the two of you cannot resolve it between yourselves.